(a) The speed of light in medium X is 2 × 10⁸ m s⁻¹ and in medium Y is 1.5 × 10⁸ m s⁻¹. Calculate the refractive index of Y with respect to X. Which medium is optically denser?
(b) A ray of light passes from medium X into medium Y. Using Snell's law, determine whether the ray bends towards or away from the normal at the interface.
(c) A convex lens of focal length 15 cm and a concave lens of focal length 30 cm are placed in contact coaxially. (i) Find the power of each lens. (ii) Find the power and focal length of the combination. (iii) State whether the combination behaves as a converging or a diverging lens.
Generated by claude-sonnet-4-6 · 2026-06-26 01:13 · grounding rag
Model Answer
(a)
Speed of light in X, $v_X = 2 \times 10^8$ m/s; in Y, $v_Y = 1.5 \times 10^8$ m/s
$$n_{YX} = \frac{v_X}{v_Y} = \frac{2 \times 10^8}{1.5 \times 10^8} = \frac{4}{3} \approx 1.33$$
Since $n_{YX} > 1$, medium Y is optically denser (higher refractive index means lower speed of light).
(b)
Since Y is optically denser than X, light slows down when passing from X into Y. According to Snell's law, the ray bends towards the normal at the interface.
(c)
- Convex lens: $f_1 = +15$ cm $= +0.15$ m → $P_1 = \dfrac{1}{0.15} = +6.67$ D
- Concave lens: $f_2 = -30$ cm $= -0.30$ m → $P_2 = \dfrac{1}{-0.30} = -3.33$ D
(ii) Net power: $P = P_1 + P_2 = 6.67 + (-3.33) = +3.33$ D
Focal length of combination: $f = \dfrac{1}{P} = \dfrac{1}{3.33} \approx +0.30$ m $= +30$ cm
(iii) Since net power is positive, the combination behaves as a converging (convex) lens.
Source: Chapter 9, Sections 9.3.2 and 9.3.8
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Explanation
- For refractive index of Y w.r.t. X, use $n_{YX} = v_X / v_Y$ (speed in the first medium divided by speed in the second).
- The medium with higher refractive index = lower speed = optically denser; light bends towards the normal entering a denser medium — a direct application of Snell's law logic.
- For lens powers: convex focal length is positive, concave is negative. Convert cm to metres before calculating power.
- Powers add algebraically; a positive net power → converging combination. Examiners expect all three sub-parts of (c) answered clearly with units.