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Refraction, Total Internal Reflection & Prisms Worksheet
By the end you will: use Snell's law and refractive index, find the critical angle, and explain how a prism splits white light.
A. Explore with the simulation
Choose Boundary mode. Set the angle of the beam to 45° going from air into each material. Fill in the table.
Material Refractive index n Angle out Speed of light (lakh km/s) Water 1.33 Glass 1.50 Diamond 2.42 Turn on “Shine from inside”. For each material, raise the angle until the light is trapped. Write down the critical angle.
Material Critical angle Water Glass Diamond Write the two conditions needed for total internal reflection.
Choose Prism mode with white light, and set the angle hitting the prism to 50°. How far does red turn? Violet? Which colour bends most?
B. Calculate (then check in the simulation)
Light goes from air into water (n = 1.33) at 30°. Find the angle of refraction.
The speed of light in a liquid is 2.25 × 10⁸ m/s. Find its refractive index. (c = 3 × 10⁸ m/s)
The refractive index of glass with respect to air is 1.5, and of water 1.33. Find the refractive index of glass with respect to water.
Find the critical angle for glass of refractive index 1.5. (sin 41.8° ≈ 0.667)
C. Think it through
Explain why (a) a pencil in water looks bent, (b) a diamond sparkles, (c) the sky's rainbow has red on the outside and violet inside.
Answer key (for teachers and parents)
- Water: 32.1°, 2.25 · Glass: 28.1°, 2.00 · Diamond: 17.0°, 1.24. The bigger n is, the more the light slows down and bends towards the normal.
- Water 48.8° · Glass 41.8° · Diamond 24.4°. Beyond it, all the light reflects back: total internal reflection.
- (1) Light must go from a denser medium into a rarer one (higher n to lower n). (2) The angle of incidence must be greater than the critical angle.
- Red turns about 38.3°, violet about 39.8°, so they spread about 1.5° apart. Violet bends most, because glass has a higher refractive index for violet light.
- sin r = sin 30° ÷ 1.33 = 0.5 ÷ 1.33 ≈ 0.376, so r ≈ 22°.
- n = c ÷ v = 3 ÷ 2.25 ≈ 1.33 (it's water).
- n(glass, water) = n(glass) ÷ n(water) = 1.5 ÷ 1.33 ≈ 1.13.
- sin c = 1 ÷ n = 1 ÷ 1.5 ≈ 0.667, so c ≈ 41.8°.
- (a) Light from the pencil bends away from the normal as it leaves the water, so the underwater part seems raised. (b) Its small critical angle (24°) traps light, which reflects many times inside before escaping. (c) Raindrops act like tiny prisms: red bends least, violet most, so they leave at different angles and reach your eye from different heights in the sky.
Free to print and share for teaching. Made with the interactive simulation at jugnix.com/simulations/refraction-prism.