JEE Challenger
More from Wave Optics

Comparison of Speed of Light Across Two Media

Comprehension Passage

The figure shows a surface XYXY separating two transparent media, medium-1 and medium-2. The lines abab and cdcd represent wavefronts of a light wave traveling in medium-1 and incident on XYXY. The lines efef and ghgh represent wavefronts of the light wave in medium-2 after refraction.

Speed of light is

Options

A

the same in medium-1 and medium-2

B

larger in medium-1 than in medium-2

Correct
C

larger in medium-2 than in medium-1

D

different at bb and dd

Step-by-Step Solution

Based on the principles of wave optics and refraction at a plane interface:

  1. Snell's Law of Refraction:
    When a light wave travels from medium-1 into medium-2, the angles of incidence (ii) and refraction (rr) are related to the speeds of light v1v_1 and v2v_2 in the respective media by:
    sin⁡isin⁡r=v1v2=n2n1\frac{\sin i}{\sin r} = \frac{v_1}{v_2} = \frac{n_2}{n_1}
    where n1n_1 and n2n_2 are the refractive indices of medium-1 and medium-2, respectively.

  2. Analysis of Refraction:
    From the given passage and wavefront diagram, the ray of light bends towards the normal upon entering medium-2 from medium-1. This implies that the angle of incidence is greater than the angle of refraction:
    i>ri > r

    Since sin⁡θ\sin \theta is a strictly increasing function for 0∘<θ<90∘0^\circ < \theta < 90^\circ:
    sin⁡i>sin⁡r  ⟹  sin⁡isin⁡r>1\sin i > \sin r \implies \frac{\sin i}{\sin r} > 1

  3. Comparison of Speeds:
    Substituting this into Snell's law:
    v1v2>1  ⟹  v1>v2\frac{v_1}{v_2} > 1 \implies v_1 > v_2

    Hence, the speed of light is larger in medium-1 than in medium-2. Furthermore, since both media are individually homogeneous and isotropic, the speed of light is uniform throughout medium-1 (including point bb) and uniform throughout medium-2 (including point dd).

Therefore, the correct statement is that the speed of light is larger in medium-1 than in medium-2.

Correct Option: (B)