Hello, and welcome to your physics lesson for today. We are diving into a fascinating topic: the refraction of light at plane surfaces. By the end of this session, you will understand why a swimming pool looks shallower than it really is, why a stick appears bent in water, and how prisms create those beautiful rainbow effects. We will explore the laws governing how light bends, learn to calculate refractive index, and discover the remarkable phenomenon of total internal reflection.
Let us begin with the fundamental concept. When light travels from one transparent medium to another—say from air into water or glass—something interesting happens at the boundary. Part of the light reflects back into the first medium, while the rest enters the second medium but changes its direction. This bending of light as it crosses from one medium to another is called refraction.
The reason light bends is simple: light travels at different speeds in different media. In vacuum, light races at 3 × 10⁸ m/s, denoted by the symbol c. In air, the speed is nearly the same. But in water, light slows down to 2.25 × 10⁸ m/s, and in glass, it travels even slower at 2 × 10⁸ m/s.
Here is the key rule to remember. When light moves from a rarer medium to a denser medium—like air to water or air to glass—it slows down and bends toward the normal. When light moves from a denser medium to a rarer medium—like glass to air—it speeds up and bends away from the normal. And if light strikes the boundary exactly perpendicular to the surface—that is, at zero degrees incidence—it passes straight through without any bending, though its speed still changes.
Now, the laws of refraction. These were first stated by the Dutch scientist Willebrord Snell, and we call them Snell's laws.
First: the incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane. Second: for a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.
Mathematically, this means sin i / sin r = constant, where the constant is the refractive index of the second medium with respect to the first, written as ₁μ₂.
Or, sin i / sin r = μ, where μ is the refractive index.
The refractive index tells us how much a medium slows down light compared to vacuum or air. We define absolute refractive index as the ratio of speed of light in vacuum to speed of light in the medium.
So, μ = c/V, where c is the speed of light in vacuum and V is the speed in the medium. The unit of refractive index is dimensionless since it is a ratio of two speeds.
Since light always slows down in any material medium, the refractive index is always greater than one. For air, it is essentially one. For water, it is 4/3 or approximately 1.33. For ordinary glass, it is 3/2 or 1.5. For diamond, it is an impressive two point four one, which explains why diamonds sparkle so brilliantly.
Let us work through a quick example. Imagine light travelling from air into glass. The refractive index of glass is one point five. If the angle of incidence is forty-five degrees, what is the angle of refraction?
Using Snell's law: sin 45° / sin r = 1.5, so sin r = sin 45° / 1.5. Since sin 45° = 1/√2, approximately 0.707, we can substitute. This gives an angle of refraction of approximately 28°. Notice how the refracted angle is smaller than the incident angle—the ray has bent toward the normal, exactly as we expect when entering a denser medium.
Now, what happens to light's properties during refraction? The frequency of light remains unchanged—it is determined by the source and stays constant. But the speed changes, and since speed equals frequency times wavelength, the wavelength must change too.
So, V = fλ, where V is speed, f is frequency, and λ is wavelength. This means wavelength in the medium equals λ' = V/f.
When light enters a denser medium, its speed decreases, so its wavelength decreases proportionally. The wavelength in the medium equals the wavelength in vacuum divided by the refractive index: λ' = λ/μ.
Here is a beautiful consequence: different colours of light have slightly different wavelengths, so they refract by slightly different amounts. Violet light, with its shorter wavelength, bends more than red light. This is why prisms split white light into a spectrum of colours.
Let us examine refraction through a rectangular glass block. When light enters one face, it bends toward the normal. It travels straight through the glass, then exits through the opposite parallel face. At the second surface, it bends away from the normal. Because the two faces are parallel, the emergent ray ends up parallel to the incident ray, but it is shifted sideways. This sideways shift is called lateral displacement.
The lateral displacement depends on three things: the thickness of the block, the angle of incidence, and the refractive index of the material. Thicker blocks produce greater displacement. Larger angles of incidence produce greater displacement. And materials with higher refractive indices produce greater displacement.
Now we turn to prisms—transparent objects with two inclined refracting surfaces. Unlike parallel-sided blocks, prisms cause the emergent ray to deviate from its original direction.
When light enters a prism, it refracts toward the normal at the first face. Inside the prism, it travels toward the second face, then refracts away from the normal upon exiting. At both refractions, the light bends toward the base of the prism.
The total angle of deviation δ depends on several factors: the angle of incidence, the refracting angle of the prism, the material of the prism, and the colour of light. For a given prism and colour, there is a special angle of incidence where the deviation is minimum. At this minimum deviation position, the ray passes symmetrically through the prism—the angle of incidence equals the angle of emergence, and the refracted ray inside runs parallel to the base of the prism.
The relationship is: i₁ + i₂ = A + δ, where i₁ is the angle of incidence, i₂ is the angle of emergence, A is the angle of the prism, and δ is the angle of deviation. At minimum deviation, i₁ = i₂ = i, so δ_min = 2i – A.
We also have: r₁ + r₂ = A, where r₁ and r₂ are the angles of refraction at the first and second faces.
Now for some everyday applications of refraction. Have you noticed how a swimming pool looks shallower than it actually is? This is because light from the bottom of the pool bends away from the normal as it exits the water. Your eye traces the light back in a straight line, creating a virtual image that appears higher than the actual bottom.
The relationship is elegant: μ = real depth/apparent depth, or equivalently, apparent depth = real depth/μ. This is why a swimming pool looks shallower than it really is.
For water with refractive index 4/3, a pool that is 4 m deep appears to be only 3 m deep when viewed from above.
Similarly, a stick partially immersed in water appears bent at the surface. The underwater portion seems raised and displaced because each point on the submerged part sends light that refracts at the water-air interface. Your brain interprets these rays as coming from a different position, creating the illusion of a bent stick.
Now we arrive at one of the most remarkable phenomena in optics: total internal reflection. This occurs when light travels from a denser medium toward a rarer medium, but only under specific conditions.
As we increase the angle of incidence in the denser medium, the refracted ray in the rarer medium bends further away from the normal. At a certain critical angle, the refracted ray skims along the surface at ninety degrees. Beyond this critical angle, no refraction occurs at all—the entire light reflects back into the denser medium.
The critical angle C relates beautifully to refractive index. We find that sin C = 1/μ, where C is the critical angle and μ is the refractive index of the denser medium with respect to the rarer medium. For absolute refractive index, this becomes μ = 1/sin C.
For glass with refractive index 1.5, the critical angle is about 41.8° or approximately 42°. For water with refractive index 4/3, it is about 48.6° or approximately 49°. For diamond, with its very high refractive index of 2.41, the critical angle is only about 25°—this is why diamonds sparkle with such intensity, as light undergoes multiple total internal reflections before emerging.
Total internal reflection requires two conditions. First, light must travel from a denser to a rarer medium. Second, the angle of incidence must exceed the critical angle. When both conditions are met, one hundred percent of the light energy reflects back—there is no loss, no absorption, no transmission. This perfect reflection makes total internal reflection far superior to ordinary reflection from mirrors.
Prisms can be designed to exploit total internal reflection in ingenious ways. A right-angled isosceles prism—with angles 45°, 45°, and 90°—can deviate light by 90° or by 180°, or it can erect an inverted image.
For 90° deviation, light enters one leg of the prism normally, travels to the hypotenuse where it strikes at 45°—beyond the critical angle—so it undergoes total internal reflection, then exits through the other leg. Periscopes use this arrangement.
For 180° deviation, light enters the hypotenuse normally, reflects off both legs through total internal reflection, then exits back through the hypotenuse in a direction opposite to the incident ray. This inverts the image and is used in binoculars and cameras.
An equilateral prism with angles 60°, 60°, and 60° can deviate light by 60° using total internal reflection.
A prism with angles 30°, 60°, and 90° can produce deviations less than 60° through a combination of total internal reflection and refraction.
Why use prisms instead of mirrors? Silvered mirrors absorb some light and tarnish over time, dimming the image. Prisms using total internal reflection deliver perfect reflection indefinitely, with no loss of brightness. The images are sharper and more brilliant.
You have now seen how refraction governs the bending of light at boundaries, how refractive index quantifies this behaviour, and how total internal reflection creates perfect mirrors from nothing more than glass and geometry. From the apparent shallowness of pools to the sparkle of diamonds, from periscopes to optical fibres, these principles illuminate our world in countless ways.
Let us recap the essential points.
First: refraction is the bending of light when it passes from one transparent medium to another, caused by the change in speed. Light bends toward the normal when entering a denser medium, and away when entering a rarer medium.
Second: Snell's law states that the ratio of sines of angles of incidence and refraction is constant, equal to the refractive index. Refractive index also equals the ratio of light speed in vacuum to light speed in the medium.
Third: when light passes through a parallel-sided block, it emerges parallel to its original direction but laterally displaced. Through a prism, light deviates toward the base, with minimum deviation occurring when the ray passes symmetrically.
Fourth: apparent depth is less than real depth, related by refractive index equals real depth over apparent depth.
Fifth: total internal reflection occurs when light in a denser medium strikes the boundary at an angle exceeding the critical angle, where sine of the critical angle equals one over the refractive index of the denser medium with respect to the rarer medium. This phenomenon enables prisms to function as perfect reflectors.
Sixth: right-angled isosceles prisms can deviate light by 90° or 180° through total internal reflection, finding applications in periscopes, binoculars, and cameras. Prisms provide perfect reflection without loss of brightness, unlike silvered mirrors.
Keep exploring, keep questioning, and remember that the behaviour of light—though invisible in itself—reveals the structure of our world in beautiful and practical ways. Until next time, stay curious.