Comparison of Speed of Light Across Two Media
The figure shows a surface separating two transparent media, medium-1 and medium-2. The lines and represent wavefronts of a light wave traveling in medium-1 and incident on . The lines and represent wavefronts of the light wave in medium-2 after refraction.
Speed of light is
Options
the same in medium-1 and medium-2
larger in medium-1 than in medium-2
larger in medium-2 than in medium-1
different at and
Topics & Concepts
Step-by-Step Solution
Based on the principles of wave optics and refraction at a plane interface:
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Snell's Law of Refraction:
When a light wave travels from medium-1 into medium-2, the angles of incidence () and refraction () are related to the speeds of light and in the respective media by:
where and are the refractive indices of medium-1 and medium-2, respectively. -
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:
Since is a strictly increasing function for :
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Comparison of Speeds:
Substituting this into Snell's law:
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 ) and uniform throughout medium-2 (including point ).
Therefore, the correct statement is that the speed of light is larger in medium-1 than in medium-2.
Correct Option: (B)