TL;DR:
Light changes speed when it enters a new material, and that makes it change direction. Snell's law:
n₁ sin θ₁ = n₂ sin θ₂.Going into a higher index (air to water), light bends toward the normal. Going into a lower index, it bends away.
Past the critical angle, light inside the denser material reflects completely: total internal reflection.
Put a straw in a glass of water and look from the side. The straw seems to snap at the surface, and the part under water looks shifted and shallower. The straw is straight. The light coming from it is what changed direction.
Light slows down, so it turns
Light travels fastest in a vacuum and slower in materials. The index of refraction n says how much slower: n = c / v, where c is the speed of light in a vacuum and v is the speed in the material. Air is very close to 1.00, and water is about 1.33, which means light in water moves at c / 1.33, about three quarters of its vacuum speed.
Why does a speed change cause a bend? Picture a marching band crossing from pavement into mud at an angle. The side that hits the mud first slows first, so the row swings around. A beam of light does the same at a boundary, and it only bends if it arrives at an angle.
Snell's law
Angles are measured from the normal, a line at right angles to the surface, not from the surface itself. Snell's law says n₁ sin θ₁ = n₂ sin θ₂, with 1 for the first material and 2 for the second.
Entering a higher index (air into water): the ray bends toward the normal, so θ₂ is smaller than θ₁.
Entering a lower index (water into air): the ray bends away from the normal.
Light hitting along the normal (θ₁ = 0) does not bend at all.
Worked example: light entering water at 40°
A ray in air hits a flat water surface at 40° to the normal. Use n = 1.00 for air and n = 1.33 for water. Find the angle in the water.
Write Snell's law:
1.00 × sin 40° = 1.33 × sin θ₂.Find
sin 40° ≈ 0.6428.Divide:
sin θ₂ = 0.6428 / 1.33 ≈ 0.4833.Take the inverse sine:
θ₂ ≈ 28.9°.
Check the direction: 28.9° is smaller than 40°, as it should be for light entering the denser material. Check the numbers by going back: 1.33 × sin 28.9° = 1.33 × 0.4833 ≈ 0.643, matching sin 40°.
Why the straw looks bent
Rays from the underwater part of the straw bend away from the normal as they leave the water. Your eye assumes light always travels in a straight line, so it traces those rays back along straight lines to a point that is shallower than the real one. The straw seems to bend upward at the surface.
For a view nearly straight down, the apparent depth is the real depth divided by n. A coin 10 cm under water seems to be at 10 / 1.33 ≈ 7.5 cm. That is why a pool looks shallower than it is, which is worth remembering before you step in.
The part of the straw in the air is seen by undisturbed rays, so it stays where it is. Only the submerged part is displaced, and that mismatch at the surface is the break you see. Rays that travel along the normal do not bend, which is why an object straight below you is not shifted sideways.
Total internal reflection
Now run the process backward: light in water heading out into air bends away from the normal. At some angle, the refracted ray would run along the surface, at 90°. This angle is the critical angle θc, and from Snell's law sin θc = n₂ / n₁.
For water to air: sin θc = 1.00 / 1.33 = 0.7519, so θc ≈ 48.8°. Beyond that angle no light escapes, and all of it reflects back into the water. This is total internal reflection. It needs light to be going from the higher index to the lower one, so it cannot happen when light enters water from air.
Optical fibres use this effect. Light stays trapped inside a glass thread by reflecting from the walls again and again, so it can follow bends.
How to check your answer
Direction. Into a higher index means a smaller angle. If your angle grew, you swapped n₁ and n₂.
Calculator mode. Make sure it is in degrees, not radians.
Reverse path. Light paths work both ways, so plug your answer in backward and see if you get the starting angle.
Impossible results. If you get
sin θbigger than 1, that is total internal reflection, not a calculator error.
Mistakes that cost marks
Measuring angles from the surface instead of the normal.
Forgetting that frequency stays the same while speed and wavelength change.
Applying the critical angle when light goes into the denser material.
Rounding sines too early. Keep four digits until the end.
Where you will use it next
Refraction is the basis of lenses, which bend light at two curved surfaces. The next step is how a magnifying glass works. It rests on the speed-wavelength link in how waves carry energy.
Frequently asked questions
Does refraction depend on colour?
Slightly. Each colour has a slightly different index in most materials, so colours bend by different amounts. That spreading is how a prism makes a rainbow.
Why do I see a mirror-like surface from under water?
Looking up at a shallow enough angle, past the critical angle, light from below reflects completely off the surface.
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