એક માધ્યમમાં પ્રકાશની ઝડપ તેની મુક્ત અવકાશની ઝડપની સરખામણીમાં \(0.2\) ભાગ જેટલી ધટે છે. આ માધ્યમ માટે સાપેક્ષ પરા વૈદ્યુતાંક અને માધ્યમના વક્રીભવનાંકનો ગુણોત્તર \(...........\) થશે.(મુક્ત અવકાશમાં પ્રકાશની ઝડપ \(=3 \times 10^8\,m s ^{-1}\) અને આપેલ માધ્યમ માટે \(\mu_{ r }=1\) આપેલ છે.)

A \(5\)
B \(4\)
C \(3\)
D \(2\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(5\)

Step-by-step Solution

Detailed explanation

\(V =\frac{ C }{\mu} \Rightarrow \mu=\frac{ C }{ V }=\frac{ C }{0.2 C }\) \(\mu=5\) \(\mu=\sqrt{\epsilon_{ r } \mu_{ r }}\) \(\Rightarrow \epsilon_{ r }=\frac{\mu^2}{\mu_{ r }}\) \(\therefore \frac{\epsilon_{ r }}{\mu}=\frac{\mu}{\mu_{ r }}=5\)

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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