Fig. 20.1 shows a ray of light travelling from glass into water. The glass has a refractive index of 1.50 and the water has a refractive index of 1.33. The ...

Marking Scheme

• (a) [1] Speed in glass \(= \frac{3.0 \times 10^8}{1.50}\). [1] \(= 2.0 \times 10^8\) m/s.
• (b) [1] Speed in water \(= \frac{3.0 \times 10^8}{1.33} = 2.26 \times 10^8\) m/s (accept \(2.3 \times 10^8\)).
• (c) [1] The light speeds up.
• (d) [1] The refracted ray bends away from the normal.
• (e) [1] \(n_1 \sin\theta_1 = n_2 \sin\theta_2\); \(1.50 \times \sin 25° = 1.33 \times \sin\theta_2\); \(\sin\theta_2 = \frac{1.50 \times 0.4226}{1.33} = 0.4766\). [1] \(\theta_2 = 28.5°\) (accept 28-29°).

Explanation

(a) The refractive index relates the speed of light in a vacuum to the speed in the medium: \(n = \frac{c}{v}\), so \(v = \frac{c}{n}\).

Speed in glass \(= \frac{3.0 \times 10^8}{1.50} = 2.0 \times 10^8\) m/s.

(b) Speed in water \(= \frac{3.0 \times 10^8}{1.33} = 2.26 \times 10^8\) m/s.

Water has a lower refractive index than glass, so light travels faster in water than in glass (but still slower than in a vacuum).

(c) Glass has a higher refractive index (1.50) than water (1.33). A higher refractive index means a slower speed. When light crosses from glass (slower) into water (faster), it speeds up.

(d) When light speeds up as it crosses a boundary, it bends away from the normal. This is because the wave fronts in the faster medium are more spread out. The ray moves from a more optically dense medium (glass) to a less optically dense medium (water), so the refracted angle is larger than the incident angle.

(e) Applying Snell's law at the glass-water boundary:

\(n_1 \sin\theta_1 = n_2 \sin\theta_2\)

\(1.50 \times \sin 25° = 1.33 \times \sin\theta_2\)

\(1.50 \times 0.4226 = 1.33 \times \sin\theta_2\)

\(\sin\theta_2 = \frac{0.6339}{1.33} = 0.4766\)

\(\theta_2 = \sin^{-1}(0.4766) = 28.5°\)

As expected, \(\theta_2 > \theta_1\) because the light is bending away from the normal as it enters the less dense medium.