Extended · Practice questions · Refractive index

Refractive index.

Six original Cambridge-style questions on the refractive index: from angles, from the critical angle, and from the speed of light. Try each fully before revealing the worked solution.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

What earns the marks here

Total internal reflection, drawn with a ruler.

Trapping. Light hits the core boundary above the critical angle, so it is totally internally reflected and stays in the core.
Drawing. The path is straight line segments meeting the boundary at sharp angles, never a curved or wavy line.
Uses. Telecommunications (high capacity, low loss) and medical endoscopes.

[2 marks]

Define what is meant by the refractive index of a material, and write down the equation that links it to the angles of incidence and refraction.

The refractive index is a measure of how much the material slows down and bends light ✓
n = sin i ÷ sin r, where i is the angle in air and r the angle in the material ✓

Analysis

[3 marks]

A ray of light passes from air into a glass block. The angle of incidence is 50 degrees and the angle of refraction is 30 degrees. Calculate the refractive index of the glass.

n = sin i ÷ sin r = sin 50 ÷ sin 30 ✓
= 0.766 ÷ 0.500 ✓
n = 1.53, about 1.5 ✓

Analysis

[3 marks]

A transparent plastic has a refractive index of 1.4. Calculate its critical angle.

sin c = 1 ÷ n = 1 ÷ 1.4 ✓
sin c = 0.714 ✓
c = 46 degrees (about 46 degrees) ✓

[2 marks]

Light travels at 3.0 × 10⁸ m/s in a vacuum and at 2.0 × 10⁸ m/s in a certain glass. Calculate the refractive index of the glass.

n = speed in vacuum ÷ speed in the medium ✓
n = (3.0 × 10⁸) ÷ (2.0 × 10⁸) = 1.5 ✓

Analysis

[3 marks]

Two materials A and B have refractive indices of 1.33 and 1.52. (a) Which material bends light more? (b) Which has the smaller critical angle? Explain your answer to part (b).

(a) Material B bends light more, because a higher refractive index means more bending ✓
(b) Material B has the smaller critical angle ✓
because sin c = 1 ÷ n, so a larger n gives a smaller critical angle ✓

Analysis

[3 marks]

A ray going from air into a glass block has an angle of incidence of 40 degrees and an angle of refraction of 25 degrees. (a) Calculate the refractive index. (b) State what happens to the frequency of the light as it enters the glass.

(a) n = sin 40 ÷ sin 25 = 0.643 ÷ 0.423 ✓
n = 1.52, about 1.5 ✓
(b) The frequency stays the same ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.