MHT CET · Physics · Ray Optics

A beam of white light is partially reflected and partially refracted from a surface. The angle between the reflected and refracted light is \(90^{\circ}\). The angle of refraction is \(30^{\circ}\). The angle of incidence must be

A \(70^{\circ}\)
B \(60^{\circ}\)
C \(55^{\circ}\)
D \(58^{\circ}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(60^{\circ}\)

Step-by-step Solution

Detailed explanation

Consider the following figure:

Take angle of incidence \(i\), angle of reflection \(r\) and angle of refraction
\(r_{\mathrm{F}}=30^{\circ}\)
Given from geometry:
\(\begin{aligned}
& r+r_{\mathrm{F}}+90^{\circ}=180^{\circ} \\
& \Rightarrow r=90^{\circ}-r_{\mathrm{F}}
\end{aligned}\)
Since, angle of incidence is equal to the angle of reflection:
\(\therefore i=r=90^{\circ}-r_F=90^{\circ}-30^{\circ}=60^{\circ}\)

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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