પ્રકાશને \(\mu_A\) અને \(\mu_B\) જેટલો વક્રીભવનાંક ઘરાવતા અને સમાન જાડાઈ ઘરાવતા જુદા-જુદા માધ્યમોમાં ગતિ કરતા લાગતો સમય અનુક્રમે \(t_1\) અને \(t_2\) છે.જો \(t _2- t _1=5 \times 10^{-10}\,s\) અને \(\mu_{ A }\) અને \(\mu_{ B }\) નો ગુણોત્તર \(1: 2\). હોય,તો દ્રવ્યની જાડાઈ મીટ૨માં શોધો. \(A\) અને \(B\) માધ્યમમાં પ્રકાશનો વેગ અનુક્રમે \(v_{ A }\) અને \(v_{ B }\) આપેલ છે.

A \(5 \times 10^{-10}\,v _{ a } m\)
B \(5 \times 10^{-10}\,m\)
C \(1.5 \times 10^{10}\,m\)
D \(5 \times 10^{-10} v _{ B }\,m\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(5 \times 10^{-10}\,v _{ a } m\)

Step-by-step Solution

Detailed explanation

\(\frac{\mu_{ A }}{\mu_{ B }}=\frac{ c / V _{ A }}{ c / V _{ B }}=\frac{ V _{ B }}{ V _{ A }}=\frac{1}{2}\) Let the thickness is \(d\) \(\frac{d}{v_{B}}-\frac{d}{v_{A}}=5 \times 10^{-10}\) \(d =\frac{5 \times 10^{-10} \times v _{ A } v _{ B }}{ v _{ A }- v _{ B }}\) As…

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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