वायु में प्रकाश \(t_1\) समय में \(x\) दूरी तथा अन्य सघन माध्यम में \(t_2\) समय में \(10 x\) दूरी तय करता है। इस माध्यम के लिए क्रान्तिक कोण क्या है ?

A \(\sin ^{-1}\left(\frac{10 t_1}{t_2}\right)\)
B \(\sin ^{-1}\left(\frac{t_2}{t_1}\right)\)
C \(\sin ^{-1}\left(\frac{10 t_2}{t_1}\right)\)
D \(\sin ^{-1}\left(\frac{t_1}{10 t_2}\right)\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\sin ^{-1}\left(\frac{10 t_1}{t_2}\right)\)

Step-by-step Solution

Detailed explanation

Speed of light is air \(V_1=\frac{x}{t_1}\) speed of light is a medium \(V_2=\frac{10 x}{t_2}\)

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.

Same subject

Match List \(- I\) with List \(- II:\)

List\(-1\) (Electromagnetic waves)	List\(-2\) (Wavelength)
\((a)\) आयाम माडुलित रेडियो तरंगें	\((i)\) \(10^{-10}\,m\)
\((b)\) सूक्ष्म तरंगें	\((ii)\) \(10^{2}\,m\)
\((c)\) अवरक्त विकिरण	\((iii)\) \(10^{-2}\,m\)
\((d)\) \(X\)-किरणें	\((iv)\) \(10^{-4}\,m\)

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