MHT CET · Physics · Ray Optics

The refractive index of the material of crystal is 1.68 and that of castor oil is 1.2. When a ray of light passes from oil to glass, its velocity will change by factor

A $\frac{2}{3}$
B $\frac{3}{4}$
C $\frac{5}{6}$
D $\frac{5}{7}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{5}{7}$

Step-by-step Solution

Detailed explanation

We know, refractive index of crystal w. r. t. oil,

μ_{c o} = \frac{μ_{c}}{μ_{o}} = \frac{s p e e d o f l i g h t i n o i l}{s p e e d o f l i g h t i n c r y s t a l}

Where,

μ_{c}

= absolute refractive index of crystal w. r. t. vacuum.
and

μ_{0}

= absolute refractive index of oil w. r. t. vacuum.

μ_{c o} = \frac{1.68}{1.2} \frac{7}{5} = \frac{s p e e d i n o i l}{s p e e d i n c r y s t a l}

Fractional change in velocity,
when light travel from oil to crystal

= \frac{s p e e d i n c r y s t a l}{s p e e d i n o i l} = \frac{5}{7}

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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