MHT CET · Physics · Ray Optics

Glass has refractive index $μ$ with respect to air and the critical angle for a ray of light going from glass to air is $θ$ . If a ray of light is incident from air on the glass with angle of incidence $θ,$ corresponding angle of refraction is

A ${s i n}^{- 1} (μ)$
B ${s i n}^{- 1} (\frac{1}{μ_{2}})$
C ${s i n}^{- 1} (\frac{1}{\sqrt{μ}})$
D ${s i n}^{- 1} (\frac{1}{μ})$

Verified Solution

Answer & Solution

Correct Answer

(B) ${s i n}^{- 1} (\frac{1}{μ_{2}})$

Step-by-step Solution

Detailed explanation

Refractive index of glass with respect to air =

μ

Critical angle =

θ

∴ μ = \frac{1}{s i n θ}

…. (i)
When a ray of light incident from air on the glass with angle of incidence

θ

. If r the angle of refraction, then by Snell’s law,

μ = \frac{s i n θ}{s i n r}

\Rightarrow s i n r = \frac{s i n θ}{μ} = \frac{1 / μ}{μ}

[from Eq. (i)]

s i n r = \frac{1}{μ^{2}}

r = {s i n}^{- 1} (\frac{1}{μ^{2}})

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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Glass has refractive index μ with respect to air and the critical angle for a ray of light going from glass to air is θ . If a ray of light is incident from air on the glass with angle of incidence θ, corresponding angle of refraction is

Step-by-step Solution

Glass has refractive index $μ$ with respect to air and the critical angle for a ray of light going from glass to air is $θ$ . If a ray of light is incident from air on the glass with angle of incidence $θ,$ corresponding angle of refraction is