{"id":297,"date":"2026-06-22T00:24:32","date_gmt":"2026-06-22T00:24:32","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=297"},"modified":"2026-06-22T00:25:46","modified_gmt":"2026-06-22T00:25:46","slug":"reflection-and-refraction","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/reflection-and-refraction\/","title":{"rendered":"Reflection and Refraction of Light"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\n\nReflection and refraction are the two ways light changes direction at a boundary between materials: reflection is when light bounces back off a surface, while refraction is when light bends as it passes through into a new medium because its speed changes. The bending follows Snell&#8217;s law, n\u2081 sin \u03b8\u2081 = n\u2082 sin \u03b8\u2082.\n\n<\/p><\/div>\n<p>Drop a straw into a glass of water and it looks snapped in half. Glance in a shop window at night and your own face stares back. Two everyday illusions, two different physics \u2014 and between them they explain mirrors, lenses, rainbows, cameras, your spectacles and the fibre\u2011optic cable carrying this page to your screen.<\/p>\n<p>Both effects happen at the same place: the boundary where one material meets another. What the light does there \u2014 bounce or bend \u2014 comes down to one question. Does it stay where it is, or does it cross over?<\/p>\n<h2>What Are Reflection and Refraction?<\/h2>\n<p>Start with the boundary. Light is travelling along happily, and it meets a surface \u2014 the face of a mirror, the top of a pond, the curve of a lens. Two things can happen, and usually both do at once.<\/p>\n<p><strong>Reflection<\/strong> is the part of the light that bounces back. It never leaves the first medium; the surface simply turns it around. A mirror reflects almost all of it, which is why you see a sharp image. <strong>Refraction<\/strong> is the part that crosses into the new medium \u2014 and as it crosses, it bends, because its speed changes.<\/p>\n<p>So reflection is a bounce and refraction is a bend. The crucial distinction is whether the light stays put or passes through.<\/p>\n<div role=\"img\" aria-label=\"Ray diagram of reflection and refraction: an incident ray hits a boundary between air and glass; it splits into a reflected ray going back into the air at an equal angle and a refracted ray that bends toward the normal as it enters the denser glass.\">\n<svg viewBox=\"0 0 600 440\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:100%;height:auto;max-width:600px;display:block;margin:0 auto;background:#FAF6EE;border-radius:6px;\">\n<defs>\n<marker id=\"arrInk\" markerWidth=\"11\" markerHeight=\"11\" refX=\"6.5\" refY=\"3\" orient=\"auto\"><path d=\"M0,0 L7,3 L0,6 Z\" fill=\"#0A1628\"><\/path><\/marker>\n<marker id=\"arrWine\" markerWidth=\"11\" markerHeight=\"11\" refX=\"6.5\" refY=\"3\" orient=\"auto\"><path d=\"M0,0 L7,3 L0,6 Z\" fill=\"#7A1F2B\"><\/path><\/marker>\n<marker id=\"arrGold\" markerWidth=\"11\" markerHeight=\"11\" refX=\"6.5\" refY=\"3\" orient=\"auto\"><path d=\"M0,0 L7,3 L0,6 Z\" fill=\"#C8932A\"><\/path><\/marker>\n<\/defs>\n<rect x=\"40\" y=\"220\" width=\"520\" height=\"180\" fill=\"#142139\" opacity=\"0.07\"><\/rect>\n<line x1=\"40\" y1=\"220\" x2=\"560\" y2=\"220\" stroke=\"#7A1F2B\" stroke-width=\"2.5\"><\/line>\n<line x1=\"300\" y1=\"45\" x2=\"300\" y2=\"400\" stroke=\"#9aa7b8\" stroke-width=\"1.6\" stroke-dasharray=\"6 5\"><\/line>\n<line x1=\"184\" y1=\"82\" x2=\"300\" y2=\"220\" stroke=\"#0A1628\" stroke-width=\"3\" marker-end=\"url(#arrInk)\"><\/line>\n<line x1=\"300\" y1=\"220\" x2=\"416\" y2=\"82\" stroke=\"#7A1F2B\" stroke-width=\"3\" marker-end=\"url(#arrWine)\"><\/line>\n<line x1=\"300\" y1=\"220\" x2=\"369\" y2=\"364\" stroke=\"#C8932A\" stroke-width=\"3\" marker-end=\"url(#arrGold)\"><\/line>\n<path d=\"M300,182 A38,38 0 0 0 275.6,190.9\" fill=\"none\" stroke=\"#0A1628\" stroke-width=\"1.4\"><\/path>\n<path d=\"M300,182 A38,38 0 0 1 324.4,190.9\" fill=\"none\" stroke=\"#7A1F2B\" stroke-width=\"1.4\"><\/path>\n<path d=\"M300,258 A38,38 0 0 0 316.3,254.3\" fill=\"none\" stroke=\"#C8932A\" stroke-width=\"1.4\"><\/path>\n<circle cx=\"300\" cy=\"220\" r=\"3.5\" fill=\"#0A1628\"><\/circle>\n<text x=\"259\" y=\"200\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"15\" fill=\"#0A1628\">\u03b8\u2081<\/text>\n<text x=\"330\" y=\"200\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"15\" fill=\"#7A1F2B\">\u03b8\u2081<\/text>\n<text x=\"332\" y=\"262\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"15\" fill=\"#9a6a1f\">\u03b8\u2082<\/text>\n<text x=\"305\" y=\"40\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#5b6b82\">Normal<\/text>\n<text x=\"92\" y=\"74\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#0A1628\">Incident ray<\/text>\n<text x=\"424\" y=\"74\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#7A1F2B\">Reflected ray<\/text>\n<text x=\"318\" y=\"388\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#9a6a1f\">Refracted ray<\/text>\n<text x=\"54\" y=\"150\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#1F2E47\">n\u2081 (air)<\/text>\n<text x=\"54\" y=\"320\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#1F2E47\">n\u2082 (glass), denser<\/text>\n<text x=\"54\" y=\"340\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12\" fill=\"#5b6b82\">n\u2082 &gt; n\u2081<\/text>\n<\/svg>\n<\/div>\n<p style=\"text-align:center;font-size:13px;color:#1F2E47;font-style:italic;\">A single ray hitting a boundary splits into a reflected ray (\u03b8\u2081 = angle of reflection) and a refracted ray (\u03b8\u2082), which bends toward the normal when it enters the denser medium.<\/p>\n<h3>Reflection vs Refraction at a Glance<\/h3>\n<p>Because these two are so often confused, here is the side\u2011by\u2011side. Notice that the deciding factor running down the table is always the same: does the light stay in one medium, or cross into another?<\/p>\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr style=\"background:#142139;color:#FAF6EE;\">\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Property<\/th>\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Reflection<\/th>\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Refraction<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>What happens<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Light bounces back off the surface<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Light passes into a new medium and changes direction<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Medium<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Stays in the same medium<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Crosses into a different medium<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Cause<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">The surface turns the wave around<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">The light&#8217;s speed changes between the two media<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Key law<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Angle of incidence = angle of reflection (\u03b8\u1d62 = \u03b8\u1d63)<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Snell&#8217;s law: n\u2081 sin \u03b8\u2081 = n\u2082 sin \u03b8\u2082<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Speed of light<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">No change<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Changes (slower in the denser medium)<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Wavelength<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Unchanged<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Changes (the frequency stays the same)<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Everyday example<\/strong><\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Your image in a mirror<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">A straw looking bent in water<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2>The Laws of Reflection and Refraction<\/h2>\n<p>Two short rules govern everything above. Both are written in terms of angles measured from the <strong>normal<\/strong> \u2014 the imaginary line drawn at right angles to the surface where the ray strikes it.<\/p>\n<h3>The Law of Reflection<\/h3>\n<p>The reflected ray leaves at the same angle it arrived. Simple, and exactly true for any smooth surface.<\/p>\n<div class=\"pf-formula\">\u03b8\u1d62 = \u03b8\u1d63<\/div>\n<ul>\n<li><strong>\u03b8\u1d62<\/strong> \u2014 angle of incidence, between the incoming ray and the normal (degrees, or radians).<\/li>\n<li><strong>\u03b8\u1d63<\/strong> \u2014 angle of reflection, between the reflected ray and the normal (degrees, or radians).<\/li>\n<\/ul>\n<h3>The Law of Refraction (Snell&#8217;s Law)<\/h3>\n<p>When light crosses into a new medium, the angle changes by an amount set by the two refractive indices. This is <a href=\"https:\/\/science.nasa.gov\/learn\/basics-of-space-flight\/chapter6-6\/#hds-sidebar-nav-1\" target=\"_blank\" rel=\"noopener\">Snell&#8217;s law<\/a>, the single most useful equation in optics.<\/p>\n<div class=\"pf-formula\">n\u2081 sin \u03b8\u2081 = n\u2082 sin \u03b8\u2082<\/div>\n<ul>\n<li><strong>n\u2081<\/strong> \u2014 refractive index of the first medium (dimensionless).<\/li>\n<li><strong>n\u2082<\/strong> \u2014 refractive index of the second medium (dimensionless).<\/li>\n<li><strong>\u03b8\u2081<\/strong> \u2014 angle of incidence in medium 1, from the normal (degrees).<\/li>\n<li><strong>\u03b8\u2082<\/strong> \u2014 angle of refraction in medium 2, from the normal (degrees).<\/li>\n<\/ul>\n<p>A common student slip is to measure the angle from the <em>surface<\/em>. Always draw the normal first, then measure from it \u2014 every formula on this page assumes that.<\/p>\n<p>The law of refraction is named after the Dutch astronomer Willebrord Snellius, who set it down in 1621; it is sometimes called the Snell\u2013Descartes law, and the same relationship was described even earlier, around 984, by the Persian scholar Ibn Sahl.<\/p>\n<h2>How Reflection and Refraction Work<\/h2>\n<p>Reflection is the easy one. Light is an electromagnetic wave, and when it meets a surface it cannot cross, the surface sends it back \u2014 like a ball off a wall, leaving at the mirror image of the angle it came in.<\/p>\n<p>Refraction is subtler, and it hinges on a single fact: <strong>light travels at different speeds in different materials.<\/strong> It is fastest in a vacuum, a touch slower in air, slower again in water, and slower still in glass or diamond.<\/p>\n<p>Why does a change in speed make the ray <em>bend<\/em>? Picture a marching band crossing from a paved road onto a muddy field at an angle. The musicians who reach the mud first slow down while the others are still on firm ground \u2014 so the whole row pivots and changes heading. Light does exactly this.<\/p>\n<p>The edge of the wavefront that enters the slower medium first gets held up, the rest catches up, and the wave swings toward the normal. Enter a slower (denser) medium and light bends <em>toward<\/em> the normal; enter a faster (less dense) medium and it bends <em>away<\/em>. NASA describes the same behaviour for light right across the electromagnetic spectrum, where the speed change at a boundary is what <a href=\"https:\/\/science.nasa.gov\/ems\/03_behaviors\/\" target=\"_blank\" rel=\"noopener\">bends light as it passes from one medium to another<\/a>.<\/p>\n<p>One detail that trips people up: if light hits the surface dead\u2011on (0\u00b0 to the normal), it still slows down \u2014 but it does <strong>not<\/strong> bend, because no part of the wavefront is held up before any other. Bending needs an angle.<\/p>\n<p>Use the lab below to fire a ray at a boundary, change the angle and the materials, and watch the reflected and refracted rays respond in real time.<\/p>\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Reflection and Refraction Lab<\/span><\/div><div class=\"pf-sim-slot-body\"><style>.pf-sim-frame{width:100%;border:none;height:600px}@media(max-width:760px){.pf-sim-frame{height:1000px}}<\/style><iframe src=\"\/labs\/reflection-refraction.html\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n<h2>Refractive Index \u2014 the Key to Bending Light<\/h2>\n<p>The refractive index, written <strong>n<\/strong>, is simply a measure of how much a material slows light down. It is the ratio of the speed of light in a vacuum to its speed in the material.<\/p>\n<div class=\"pf-formula\">n = c \/ v<\/div>\n<ul>\n<li><strong>n<\/strong> \u2014 refractive index of the material (dimensionless).<\/li>\n<li><strong>c<\/strong> \u2014 speed of light in a vacuum, 299,792,458 m\/s (about 3.00 \u00d7 10\u2078 m\/s).<\/li>\n<li><strong>v<\/strong> \u2014 speed of light in the material (m\/s).<\/li>\n<\/ul>\n<p>A vacuum has n = 1 exactly. Everything ordinary has n greater than 1, because light always slows in matter. The bigger the index, the slower the light and the harder it bends. Diamond&#8217;s enormous index of 2.42 is the whole reason it dazzles.<\/p>\n<p><strong>Sanity check:<\/strong> light slows in any normal material, so n for glass, water or diamond is always above 1. If your arithmetic ever hands you n &lt; 1 for these, you&#8217;ve flipped the c\/v ratio.<\/p>\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr style=\"background:#142139;color:#FAF6EE;\">\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Material<\/th>\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Refractive index (n)<\/th>\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Speed of light inside (approx.)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Vacuum<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">1.0000<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">3.00 \u00d7 10\u2078 m\/s<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Air<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">1.0003<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">\u2248 3.00 \u00d7 10\u2078 m\/s<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Water<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">1.33<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">2.26 \u00d7 10\u2078 m\/s<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Ice<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">1.31<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">2.29 \u00d7 10\u2078 m\/s<\/td>\n<\/tr>\n<tr>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Glass (typical)<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">1.50<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">2.00 \u00d7 10\u2078 m\/s<\/td>\n<\/tr>\n<tr style=\"background:#F5F2EA;\">\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">Diamond<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">2.42<\/td>\n<td style=\"padding:10px;border:1px solid #D9CFB8;\">1.24 \u00d7 10\u2078 m\/s<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>These figures are approximate, and n shifts very slightly with the colour of the light \u2014 a detail that turns out to matter enormously, as we&#8217;ll see with rainbows. The measured indices for these common materials are catalogued in this <a href=\"https:\/\/eng.libretexts.org\/Bookshelves\/Materials_Science\/Supplemental_Modules_(Materials_Science)\/Optical_Properties\/Snell&#039;s_Law\" target=\"_blank\" rel=\"noopener\">LibreTexts reference on Snell&#8217;s law<\/a>.<\/p>\n<p>Because n is tied to speed, the slowing of light depends ultimately on the fixed <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/modern-physics\/speed-of-light\/\">speed of light<\/a> in a vacuum \u2014 the c at the top of that fraction.<\/p>\n<h2>Total Internal Reflection and the Critical Angle<\/h2>\n<p>Here is where reflection and refraction stop being separate stories and merge into one. Send light the &#8220;wrong way&#8221; \u2014 from a dense medium toward a less dense one, say from water up into air \u2014 and the refracted ray bends away from the normal. Tilt the ray more, and the refracted ray bends flatter and flatter.<\/p>\n<p>At one special angle, the <strong>critical angle<\/strong>, the refracted ray skims right along the surface at 90\u00b0. Push past it, and refraction vanishes entirely: <em>all<\/em> the light reflects back inside. This is <strong>total internal reflection<\/strong>.<\/p>\n<div class=\"pf-formula\">sin \u03b8c = n\u2082 \/ n\u2081<\/div>\n<ul>\n<li><strong>\u03b8c<\/strong> \u2014 critical angle, measured from the normal (degrees). Only exists when n\u2081 &gt; n\u2082.<\/li>\n<li><strong>n\u2081<\/strong> \u2014 refractive index of the denser medium the light starts in (dimensionless).<\/li>\n<li><strong>n\u2082<\/strong> \u2014 refractive index of the less dense medium (dimensionless).<\/li>\n<\/ul>\n<p>For a water\u2013air boundary the critical angle is about 48.8\u00b0; for ordinary glass to air, about 41\u00b0; for diamond, a tiny 24.4\u00b0. The smaller that angle, the more easily light gets trapped \u2014 which is precisely why a cut diamond holds onto light and throws it back at you in flashes.<\/p>\n<div role=\"img\" aria-label=\"Total internal reflection diagram: three rays travel from a source in a denser medium up to the boundary. The first hits below the critical angle and refracts out into the less dense medium, bending away from the normal. The second hits at the critical angle and the refracted ray grazes along the surface. The third hits beyond the critical angle and reflects entirely back into the denser medium.\">\n<svg viewBox=\"0 0 600 380\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:100%;height:auto;max-width:600px;display:block;margin:0 auto;background:#FAF6EE;border-radius:6px;\">\n<defs>\n<marker id=\"arrG2\" markerWidth=\"11\" markerHeight=\"11\" refX=\"6.5\" refY=\"3\" orient=\"auto\"><path d=\"M0,0 L7,3 L0,6 Z\" fill=\"#C8932A\"><\/path><\/marker>\n<marker id=\"arrInk2\" markerWidth=\"11\" markerHeight=\"11\" refX=\"6.5\" refY=\"3\" orient=\"auto\"><path d=\"M0,0 L7,3 L0,6 Z\" fill=\"#0A1628\"><\/path><\/marker>\n<\/defs>\n<rect x=\"40\" y=\"170\" width=\"520\" height=\"180\" fill=\"#142139\" opacity=\"0.08\"><\/rect>\n<line x1=\"40\" y1=\"170\" x2=\"560\" y2=\"170\" stroke=\"#7A1F2B\" stroke-width=\"2.5\"><\/line>\n<line x1=\"180\" y1=\"120\" x2=\"180\" y2=\"220\" stroke=\"#9aa7b8\" stroke-width=\"1.3\" stroke-dasharray=\"5 4\"><\/line>\n<line x1=\"293\" y1=\"120\" x2=\"293\" y2=\"220\" stroke=\"#9aa7b8\" stroke-width=\"1.3\" stroke-dasharray=\"5 4\"><\/line>\n<line x1=\"387\" y1=\"120\" x2=\"387\" y2=\"220\" stroke=\"#9aa7b8\" stroke-width=\"1.3\" stroke-dasharray=\"5 4\"><\/line>\n<line x1=\"110\" y1=\"330\" x2=\"180\" y2=\"170\" stroke=\"#0A1628\" stroke-width=\"2.6\" marker-end=\"url(#arrInk2)\"><\/line>\n<line x1=\"110\" y1=\"330\" x2=\"293\" y2=\"170\" stroke=\"#0A1628\" stroke-width=\"2.6\" marker-end=\"url(#arrInk2)\"><\/line>\n<line x1=\"110\" y1=\"330\" x2=\"387\" y2=\"170\" stroke=\"#0A1628\" stroke-width=\"2.6\" marker-end=\"url(#arrInk2)\"><\/line>\n<line x1=\"180\" y1=\"170\" x2=\"244\" y2=\"69\" stroke=\"#C8932A\" stroke-width=\"2.6\" marker-end=\"url(#arrG2)\"><\/line>\n<line x1=\"180\" y1=\"170\" x2=\"204\" y2=\"226\" stroke=\"#7A1F2B\" stroke-width=\"1.4\" opacity=\"0.4\"><\/line>\n<line x1=\"293\" y1=\"170\" x2=\"413\" y2=\"170\" stroke=\"#C8932A\" stroke-width=\"2.6\" marker-end=\"url(#arrG2)\"><\/line>\n<line x1=\"293\" y1=\"170\" x2=\"317\" y2=\"226\" stroke=\"#7A1F2B\" stroke-width=\"1.4\" opacity=\"0.4\"><\/line>\n<line x1=\"387\" y1=\"170\" x2=\"508\" y2=\"240\" stroke=\"#C8932A\" stroke-width=\"3\" marker-end=\"url(#arrG2)\"><\/line>\n<circle cx=\"110\" cy=\"330\" r=\"4\" fill=\"#0A1628\"><\/circle>\n<text x=\"120\" y=\"345\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12\" fill=\"#1F2E47\">Light source<\/text>\n<text x=\"200\" y=\"60\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12\" fill=\"#9a6a1f\">\u03b8 &lt; \u03b8c: refracts out<\/text>\n<text x=\"338\" y=\"158\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12\" fill=\"#9a6a1f\">\u03b8 = \u03b8c: grazes surface<\/text>\n<text x=\"404\" y=\"258\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12\" fill=\"#7A1F2B\">\u03b8 &gt; \u03b8c: total internal reflection<\/text>\n<text x=\"50\" y=\"150\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#1F2E47\">n\u2081 (air, less dense)<\/text>\n<text x=\"50\" y=\"205\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#1F2E47\">n\u2082 (water, denser) \u2014 n\u2082 &gt; n\u2081<\/text>\n<\/svg>\n<\/div>\n<p style=\"text-align:center;font-size:13px;color:#1F2E47;font-style:italic;\">As the angle of incidence in the denser medium grows, the escaping ray bends flatter, grazes the surface at the critical angle \u03b8c, and beyond it is reflected entirely \u2014 total internal reflection. (Faint rays show the partial reflection that always accompanies refraction.)<\/p>\n<h2>Real\u2011World Examples of Reflection and Refraction<\/h2>\n<p>Once you know what to look for, these two effects are everywhere.<\/p>\n<h3>Mirrors and your reflection<\/h3>\n<p>A mirror is a sheet of glass backed with metal so smooth that it reflects almost every ray. Because the reflection is even, the rays keep their arrangement and you see a crisp image of yourself.<\/p>\n<h3>The bent straw<\/h3>\n<p>The straw that looks broken at the waterline isn&#8217;t bent at all. Light from the submerged part refracts as it leaves the water, so your eyes trace it back along the wrong line \u2014 and the straw appears to jump sideways.<\/p>\n<figure style=\"margin:32px auto;max-width:600px;text-align:center;\">\n  <img decoding=\"async\" src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/06\/4e09c831b679acd291971d7eed9c0a22.jpg\"\n       alt=\"Straw appearing bent in a glass of water due to refraction of light\"\n       loading=\"lazy\"\n       style=\"width:100%;height:auto;border-radius:4px;\" \/>\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">\n    The straw is perfectly straight \u2014 refraction at the water surface shifts the submerged part sideways, creating the classic &#8220;broken straw&#8221; illusion.\n  <\/figcaption>\n<\/figure>\n<h3>Rainbows<\/h3>\n<p>A raindrop is a tiny lens. Sunlight refracts going in, reflects off the back, and refracts again coming out. Because each colour bends by a slightly different amount, the white light fans out into the familiar arc of red through violet.<\/p>\n<h3>Optical fibres<\/h3>\n<p>The internet runs on total internal reflection. Light pulses fired down a hair\u2011thin glass fibre strike the walls beyond the critical angle every time, so they bounce along the inside for kilometres without leaking out \u2014 carrying data at the speed of light.<\/p>\n<h3>Lenses<\/h3>\n<p>Spectacles, cameras, microscopes and telescopes all bend light on purpose. A curved lens refracts every ray that passes through by just the right angle to bring them to a focus, sharpening a blurred world or magnifying a distant one.<\/p>\n<h2>Common Misconceptions About Reflection and Refraction<\/h2>\n<p>A few stubborn misunderstandings are worth clearing up.<\/p>\n<h3>&#8220;Reflection only happens with mirrors.&#8221;<\/h3>\n<p>Every surface reflects some light \u2014 that&#8217;s how you see this page, a wall, or a wooden table, none of which glow on their own. Rough surfaces simply scatter the reflection in all directions (diffuse reflection) instead of returning a clean image.<\/p>\n<h3>&#8220;All refraction bends the light.&#8221;<\/h3>\n<p>Only refraction <em>at an angle<\/em> bends it. Light striking a surface straight on still slows down as it enters the new medium, but it carries straight through without changing direction.<\/p>\n<h3>&#8220;The angle is measured from the surface.&#8221;<\/h3>\n<p>It is always measured from the normal \u2014 the perpendicular to the surface. Mixing this up flips your numbers; an angle of 30\u00b0 from the surface is 60\u00b0 from the normal, and Snell&#8217;s law wants the latter.<\/p>\n<h3>&#8220;Light always bends toward the normal.&#8221;<\/h3>\n<p>It only bends toward the normal when entering a <em>denser<\/em> medium. Going the other way \u2014 from glass or water out into air \u2014 it bends <em>away<\/em> from the normal, and at a steep enough angle it doesn&#8217;t escape at all.<\/p>\n<h2>How Reflection and Refraction Relate to Other Wave Concepts<\/h2>\n<p>Light is a wave, so everything here is a special case of wider wave behaviour. Reflection and refraction happen for sound and water waves too \u2014 but light makes them easy to see.<\/p>\n<p>The fact that light is a <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/transverse-vs-longitudinal-waves\/\">transverse wave<\/a> underlies its whole personality, including how it reflects and polarises. And the rule that the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/frequency-formula\/\">frequency<\/a> of a wave stays fixed while its speed changes is exactly why the wavelength shrinks in glass while the colour stays the same.<\/p>\n<p>That same wave\u2011speed thinking drives a different effect entirely. When a source moves, the apparent frequency shifts \u2014 the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/doppler-effect\/\">Doppler effect<\/a> \u2014 a useful contrast, because there the wave bends in frequency rather than in direction.<\/p>\n<h2>Worked Problems<\/h2>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 1<\/div><div class=\"pf-problem-question\">A ray of light strikes a flat mirror at an angle of incidence of 32\u00b0 (measured from the normal). What is the angle of reflection?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>Step 1:<\/strong> Apply the law of reflection, \u03b8\u1d62 = \u03b8\u1d63.<\/p>\n<p><strong>Step 2:<\/strong> The angle of incidence is 32\u00b0, so the angle of reflection equals it directly.<\/p>\n<p><strong>Answer: 32\u00b0 from the normal.<\/strong><\/p>\n<\/div><\/details><\/div>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 2<\/div><div class=\"pf-problem-question\">Light hits a flat mirror, making an angle of 25\u00b0 with the mirror&#039;s surface. What is the angle of reflection, measured from the normal?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>Step 1:<\/strong> The normal is perpendicular to the surface, so convert: angle of incidence = 90\u00b0 \u2212 25\u00b0 = 65\u00b0.<\/p>\n<p><strong>Step 2:<\/strong> By the law of reflection, \u03b8\u1d63 = \u03b8\u1d62 = 65\u00b0.<\/p>\n<p><strong>Answer: 65\u00b0 from the normal.<\/strong> (Always measure from the normal, never the surface.)<\/p>\n<\/div><\/details><\/div>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">Light passes from air (n\u2081 = 1.00) into glass (n\u2082 = 1.50) at an angle of incidence of 30\u00b0. Find the angle of refraction.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>Step 1:<\/strong> Use Snell&#8217;s law: n\u2081 sin \u03b8\u2081 = n\u2082 sin \u03b8\u2082.<\/p>\n<p><strong>Step 2:<\/strong> Substitute: (1.00)(sin 30\u00b0) = (1.50)(sin \u03b8\u2082), so (1.00)(0.5000) = 1.50 sin \u03b8\u2082.<\/p>\n<p><strong>Step 3:<\/strong> sin \u03b8\u2082 = 0.5000 \/ 1.50 = 0.3333, so \u03b8\u2082 = sin\u207b\u00b9(0.3333) = 19.5\u00b0.<\/p>\n<p><strong>Answer: 19.5\u00b0 from the normal<\/strong> \u2014 bent toward the normal, as expected entering a denser medium.<\/p>\n<\/div><\/details><\/div>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">Light travels at 2.00 \u00d7 10\u2078 m\/s inside a transparent plastic. Taking c = 3.00 \u00d7 10\u2078 m\/s, find the refractive index of the plastic.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>Step 1:<\/strong> Use n = c \/ v.<\/p>\n<p><strong>Step 2:<\/strong> Substitute: n = (3.00 \u00d7 10\u2078 m\/s) \/ (2.00 \u00d7 10\u2078 m\/s).<\/p>\n<p><strong>Step 3:<\/strong> n = 1.50.<\/p>\n<p><strong>Answer: n = 1.50<\/strong> (dimensionless \u2014 the units of speed cancel).<\/p>\n<\/div><\/details><\/div>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">The refractive index of water is 1.33. Taking c = 3.00 \u00d7 10\u2078 m\/s, find the speed of light in water.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>Step 1:<\/strong> Rearrange n = c \/ v to give v = c \/ n.<\/p>\n<p><strong>Step 2:<\/strong> Substitute: v = (3.00 \u00d7 10\u2078 m\/s) \/ 1.33.<\/p>\n<p><strong>Step 3:<\/strong> v = 2.26 \u00d7 10\u2078 m\/s.<\/p>\n<p><strong>Answer: 2.26 \u00d7 10\u2078 m\/s<\/strong> \u2014 about three\u2011quarters of its vacuum speed.<\/p>\n<\/div><\/details><\/div>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">Light passes from water (n\u2081 = 1.33) out into air (n\u2082 = 1.00) at an angle of incidence of 30\u00b0. Find the angle of refraction.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>Step 1:<\/strong> Apply Snell&#8217;s law: n\u2081 sin \u03b8\u2081 = n\u2082 sin \u03b8\u2082.<\/p>\n<p><strong>Step 2:<\/strong> Substitute: (1.33)(sin 30\u00b0) = (1.00)(sin \u03b8\u2082), so (1.33)(0.5000) = sin \u03b8\u2082.<\/p>\n<p><strong>Step 3:<\/strong> sin \u03b8\u2082 = 0.6650, so \u03b8\u2082 = sin\u207b\u00b9(0.6650) = 41.7\u00b0.<\/p>\n<p><strong>Answer: 41.7\u00b0 from the normal<\/strong> \u2014 bent away from the normal, because the light is entering a less dense medium.<\/p>\n<\/div><\/details><\/div>\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 7<\/div><div class=\"pf-problem-question\">A diamond has a refractive index of 2.42. (a) Find the critical angle for a diamond\u2013air boundary. (b) Explain why this gives a cut diamond its sparkle.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>Step 1:<\/strong> Use the critical\u2011angle formula: sin \u03b8c = n\u2082 \/ n\u2081, with n\u2081 = 2.42 (diamond) and n\u2082 = 1.00 (air).<\/p>\n<p><strong>Step 2:<\/strong> sin \u03b8c = 1.00 \/ 2.42 = 0.4132, so \u03b8c = sin\u207b\u00b9(0.4132) = 24.4\u00b0.<\/p>\n<p><strong>Step 3 (part b):<\/strong> Because the critical angle is only about 24\u00b0, light entering the diamond meets most internal faces at more than 24.4\u00b0 and is totally internally reflected. It bounces around inside many times before escaping, emerging in bright flashes.<\/p>\n<p><strong>Answer: critical angle \u2248 24.4\u00b0; the small angle traps light by total internal reflection, producing the diamond&#8217;s brilliance.<\/strong><\/p>\n<\/div><\/details><\/div>\n<h2>Frequently Asked Questions<\/h2>\n<details class=\"pf-faq-item\"><summary>What is the difference between reflection and refraction?<\/summary><div class=\"pf-faq-item-answer\">\n\nReflection is light bouncing back off a surface, staying in the same medium; refraction is light bending as it passes through into a new medium. The deciding factor is whether the light crosses the boundary or not. Reflection follows \u03b8\u1d62 = \u03b8\u1d63, while refraction follows Snell&#8217;s law, n\u2081 sin \u03b8\u2081 = n\u2082 sin \u03b8\u2082.\n\n<\/div><\/details>\n<details class=\"pf-faq-item\"><summary>Why does light bend when it enters water or glass?<\/summary><div class=\"pf-faq-item-answer\">\n\nLight bends because it changes speed at the boundary. It travels slower in water or glass than in air, and when the ray hits the surface at an angle, one edge of the wavefront slows before the other, swinging the whole ray toward the normal. Hit the surface straight on and it slows but does not bend.\n\n<\/div><\/details>\n<details class=\"pf-faq-item\"><summary>Does the frequency or wavelength of light change during refraction?<\/summary><div class=\"pf-faq-item-answer\">\n\nThe frequency stays the same; the wavelength changes. The number of waves reaching the boundary each second must equal the number leaving it, so the frequency is fixed. Since wave speed = frequency \u00d7 wavelength and the speed drops in the denser medium, the wavelength shrinks. That is why the colour of light does not change as it enters glass.\n\n<\/div><\/details>\n<details class=\"pf-faq-item\"><summary>What is total internal reflection?<\/summary><div class=\"pf-faq-item-answer\">\n\nTotal internal reflection is when light hits a boundary from the denser side at more than the critical angle and reflects entirely back, with none escaping. It only happens going from a higher\u2011index medium to a lower\u2011index one \u2014 such as water to air or glass to air. Optical fibres rely on it to carry light over long distances.\n\n<\/div><\/details>\n<details class=\"pf-faq-item\"><summary>Why does a straw look bent in a glass of water?<\/summary><div class=\"pf-faq-item-answer\">\n\nThe straw looks bent because light from its submerged part refracts as it leaves the water and enters the air. Your eyes assume light travels in straight lines, so they trace the bent rays back to the wrong position, making the underwater part appear shifted. The straw itself is perfectly straight \u2014 the illusion is pure refraction.\n\n<\/div><\/details>\n<details class=\"pf-faq-item\"><summary>What is Snell&#039;s law in simple terms?<\/summary><div class=\"pf-faq-item-answer\">\n\nSnell&#8217;s law says that when light crosses a boundary, the product of the refractive index and the sine of the angle is the same on both sides: n\u2081 sin \u03b8\u2081 = n\u2082 sin \u03b8\u2082. In plain words, it predicts exactly how much a ray bends from the two materials&#8217; refractive indices and the incoming angle, all measured from the normal.\n\n<\/div><\/details>\n","protected":false},"excerpt":{"rendered":"<p>Reflection and refraction explained simply, with the laws, Snell&#8217;s law, refractive index, total internal reflection, worked examples, and an interactive lab.<\/p>\n","protected":false},"author":1,"featured_media":298,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[151,152,153,150,154],"class_list":["post-297","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-waves","tag-reflection","tag-refraction","tag-refractive-index","tag-snells-law","tag-total-internal-reflection"],"_links":{"self":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/297","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/comments?post=297"}],"version-history":[{"count":4,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/297\/revisions"}],"predecessor-version":[{"id":303,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/297\/revisions\/303"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/298"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=297"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=297"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}