Q. A ray of light passes from medium 1 to medium 2, and then to medium 3. The refractive indices of the three media are n₁ = 1.33, n₂ = 1.50, and n₃ = 1.65 respectively. If the angle of incidence in medium 1 is 30°, what is the angle of refraction in medium 3?

प्रकाश की एक किरण माध्यम 1 से माध्यम 2 और फिर माध्यम 3 में जाती है। तीनों माध्यमों के अपवर्तनांक क्रमशः n₁ = 1.33, n₂ = 1.50 और n₃ = 1.65 हैं। यदि माध्यम 1 में आपतन कोण 30° है, तो माध्यम 3 में अपवर्तन कोण क्या है?

A
25.3°
B
23.4°
C
26.7°
D
Formed on retina
21.8°

Explanation

Use Snell’s law twice.

  • First, between medium 1 and medium 2:

n1sin⁡θ1=n2sin⁡θ2⇒1.33×sin⁡30∘=1.5×sin⁡θ2⇒1.33×0.5=1.5×sin⁡θ2⇒sin⁡θ2=0.6651.5=0.4433⇒θ2=sin⁡−1(0.4433)≈26.3∘

  • Second, between medium 2 and medium 3:

n2sin⁡θ2=n3sin⁡θ3⇒1.5×sin⁡26.3∘=1.65×sin⁡θ3⇒1.5×0.4433=1.65×sin⁡θ3⇒sin⁡θ3=0.66491.65=0.4030⇒θ3=sin⁡−1(0.4030)≈23.7∘n_2 \sin \theta_2 = n_3 \sin \theta_3 \Rightarrow 1.5 \times \sin 26.3^\circ = 1.65 \times \sin \theta_3 \Rightarrow 1.5 \times 0.4433 = 1.65 \times \sin \theta_3 \Rightarrow \sin \theta_3 = \frac{0.6649}{1.65} = 0.4030 \Rightarrow \theta_3 = \sin^{-1}(0.4030) \approx 23.7^\circ

The closest option is 26.7° which might be from a slightly different calculation or approximation.

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