MHT CET · Physics · Ray Optics

A ray of light is incident at an angle of incidence 'i' on one surface of a thin prism of
small angle 'A'. The ray emerges normally from the opposite surface. If the refractive
index of the material of the prism is ' \(\mu\) ', the angle of incidence 'i' is nearly equal to

A \(\underline{A}\)
B \(\frac{\mu A}{2}\)
C \(\mu A\)
D \(\frac{A}{2 \mu}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\mu A\)

Step-by-step Solution

Detailed explanation

\(\mu=\frac{\sin \mathrm{i}}{\sin \mathrm{r}}=\frac{\mathrm{i}}{\mathrm{r}_{1}} \quad\) if angles are small.
\(A=r_{1}+r_{2}=r_{1}\)
since \(r_{2}=0\) since the ray emerges normally.
\(\therefore \mu=\frac{i}{A} \quad\) or \(\quad i=\mu A\)

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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A ray of light is incident at an angle of incidence 'i' on one surface of a thin prism ofsmall angle 'A'. The ray emerges normally from the opposite surface. If the refractiveindex of the material of the prism is ' \(\mu\) ', the angle of incidence 'i' is nearly equal to

Step-by-step Solution

A ray of light is incident at an angle of incidence 'i' on one surface of a thin prism of
small angle 'A'. The ray emerges normally from the opposite surface. If the refractive
index of the material of the prism is ' \(\mu\) ', the angle of incidence 'i' is nearly equal to