A) \[\frac{n}{d(n+\sqrt{2})}\]
B) \[\frac{d\,(n+\sqrt{2})}{n\sqrt{2}}\]
C) \[\frac{\sqrt{2}n}{d\,(n+\sqrt{2})}\]
D) \[\frac{nd}{d+\sqrt{2}n}\]
Correct Answer: B
Solution :
Refractive index \[=\frac{Rea1\text{ }depth\text{ (}d\text{)}}{Apparent\text{ }depth\text{ (}x\text{)}}\] For 1st liquid, \[\sqrt{2}=\frac{d}{{{x}_{1}}}\] \[\Rightarrow \] \[{{x}_{1}}=\frac{d}{\sqrt{2}}\] Similarly, for 2nd liquid, \[n=\frac{d}{\sqrt{2}}\] \[\Rightarrow \] \[{{x}_{2}}=\frac{d}{n}\] Total apparent depth \[={{x}_{1}}+{{x}_{2}}\] \[=\frac{d}{\sqrt{2}}+\frac{d}{n}\] \[=\frac{d\,(n+\sqrt{2})}{n\,\sqrt{2}}\]
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