આકૃતિમાં દર્શાવ્યા પ્રમાણે એક \(AO\) પ્રકાશનું કિરણ શૂન્યાવકાશમાથી કાચમાં \(60^o\)ના ખુણે આપાત થઈને કિરણ \(OB\) \(30^o\)ના ખૂણે વક્રીભવન પામે છે.\(A\) થી \(B\) સુધીનો પ્રકાશિય પથ કેટલો થાય?

A \(2a + \frac{{2b}}{{\sqrt 3 }}\)
B \(2a + \frac{{2b}}{3}\)
C \(\frac{{2\sqrt 3 }}{a} + 2b\)
D \(2a + 2b\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(2a + 2b\)

Step-by-step Solution

Detailed explanation

From Snell's law \(1 \sin 60^o=\mu \sin 30^o\) \(\Rightarrow \mu=\sqrt{3}\) Optical path \( = {\text{AO}} + \mu ({\text{OB}})\) \( = \frac{{\text{a}}}{{\cos {{60}^o}}} + \sqrt 3 \frac{{\text{b}}}{{\cos {{30}^o}}}\) \( = 2{\text{a}} + 2{\text{b}}\)

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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