MHT CET · Physics · Ray Optics

The critical angle for light going from medium ‘x’ to medium ‘y’ is $' θ^{'}$ . The speed of light in medium ‘x’ is $' v_{x}^{'}$ . The speed of light in medium ‘y’ is

A $\frac{v_{x}}{t a n θ}$
B $v_{x} s i n θ$
C $v_{x} t a n θ$
D $\frac{v_{x}}{s i n θ}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{v_{x}}{s i n θ}$

Step-by-step Solution

Detailed explanation

The critical angle is that angle on incidence in the denser medium for which the angle of refraction in rarer medium is

90^{o}, i . e .

\frac{s i n θ}{s i n 90^{o}} = \frac{μ_{y}}{μ_{x}}

\Rightarrow s i n θ = \frac{μ_{y}}{μ_{x}}

…. (i)
Where,

μ =

refractive index of medium.

A l s o, μ = \frac{s p e e d o f l i g h t i n v a c u u m}{s p e e d o f l i g h t i n m e d i u m} = \frac{c}{v}

… (ii)
Form Eqs. (i) and (ii), we get

s i n θ \frac{c}{v_{y}} \times \frac{v_{x}}{c} = \frac{v_{x}}{v_{y}} \Rightarrow v_{y} = \frac{v_{x}}{s i n θ}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Step-by-step Solution

The critical angle for light going from medium ‘x’ to medium ‘y’ is $' θ^{'}$ . The speed of light in medium ‘x’ is $' v_{x}^{'}$ . The speed of light in medium ‘y’ is