NEET · Physics · STD 12 - 9. Ray optics and optical instruments

The angle of incidence for a ray of light at a refracting surface of a prism is \(45^o \). The angle of prism is \(60^o \) . If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are

A \(30^o \),\(\sqrt 2 \)
B \(45^o \),\(\sqrt 2 \)
C \(30^o \),\(\frac{1}{{\sqrt 2 }}\)
D \(45^o \),\(\frac{1}{{\sqrt 2 }}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(30^o \),\(\sqrt 2 \)

Step-by-step Solution

Detailed explanation

Given, \(i=45^o\) , \(A=60^o\) since the ray undergoes minimum deviation, therefore, angle of emergence from second face, \(e=i=45^o\)

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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