Seven original Cambridge-style questions. They cover calculations in both directions, the n = 1/sin c link, and the three things that turn a correct method into a wrong answer: inverting the ratio, radians mode, and early rounding.
Write down the two formulae that connect the refractive index n to (a) the angles of incidence and refraction, and (b) the critical angle c.
(a) n = sin i / sin r
(b) n = 1 / sin c
Both are on the data list, but you must know which angle goes where.
A ray of light passes from air into a glass block. The angle of incidence is 42° and the angle of refraction is 27°. Calculate the refractive index of the glass.
Formula:
n = sin i / sin r = sin 42° / sin 27°Sines (full precision): sin 42° = 0.6691, sin 27° = 0.4540
n = 0.6691 / 0.4540 = 1.474n = 1.47
Greater than 1, as a refractive index must be. Round only here, not at the sines.
The refractive index of water is 1.33. A ray of light enters water from air with an angle of incidence of 40°. Calculate the angle of refraction in the water.
Rearrange: n = sin i / sin r, so sin r = sin i / n
sin r = sin 40° / 1.33 = 0.6428 / 1.33 sin r = 0.4833 r = sin⁻¹(0.4833) = 28.9°r = 28.9°
r is smaller than i, so the ray bends toward the normal entering the denser water. Sense check passed.
A ray of light travels from inside a glass block out into the air. The angle in the glass is 28° and the angle in the air is 45°. A student calculates the refractive index as sin 28° / sin 45° = 0.66.
(a) Explain how you can tell, without a calculator, that 0.66 must be wrong. [1] (b) Calculate the correct refractive index. [2](a) A refractive index is always greater than 1. A value of 0.66 is impossible, so the ratio has been inverted. ✓
(b) The less dense medium (air) angle goes on top:
n = sin 45° / sin 28° = 0.7071 / 0.4695 = 1.51n = 1.51 ✓✓
Direction of travel does not matter. Air angle on top, every time.
A type of glass has a refractive index of 1.50.
(a) Calculate the critical angle for this glass. [2] (b) A ray inside the glass meets the surface at 45°. State whether it refracts out or is totally internally reflected. [1](a) sin c = 1 / n = 1 / 1.50 = 0.6667
c = sin⁻¹(0.6667) = 41.8°c = 41.8° ✓✓
(b) 45° is greater than the critical angle 41.8°, so the ray is totally internally reflected. ✓
Two students each calculate the refractive index of a glass block using i = 50° and r = 31°. One gets 1.49, the other gets 0.94. The correct answer is 1.49.
Suggest the single most likely mistake the second student made, and explain how to avoid it.
A method that is perfectly correct still scores zero in the wrong calculator mode. Check DEG first.
The refractive indices of three materials are: water 1.33, glass 1.50, diamond 2.42.
(a) For the same angle of incidence in air, which material bends the light the most? Explain. [1] (b) Which material has the smallest critical angle? [1](a) Diamond, because it has the highest refractive index, so it slows and bends the light the most. ✓
(b) Diamond, since a larger n gives a smaller critical angle (n = 1/sin c). ✓
Higher n means stronger bending and easier total internal reflection. That is the optics of a diamond's sparkle.