A) \[\frac{n}{d\left( n+\sqrt{2} \right)}\]
B) \[\frac{d\left( n+\sqrt{2} \right)}{n\sqrt{2}}\]
C) \[\frac{\sqrt{2}n}{d\left( n+\sqrt{2} \right)}\]
D) \[\frac{nd}{d+\sqrt{2n}}\]
Correct Answer: B
Solution :
Refractive index \[\mu =\frac{\text{Real}\,\text{depth(d)}}{\text{Apparent}\,\text{depth(x)}}\] For 1st liquid, \[\sqrt{2}=\frac{d}{{{x}_{1}}}\] \[\Rightarrow \] \[{{x}_{1}}=\frac{d}{\sqrt{2}}\] Similarly, for 2nd liquid, \[n=\frac{d}{{{x}_{2}}}\] \[\Rightarrow \] \[{{x}_{2}}=\frac{d}{n}\] Total apparent depth \[={{x}_{1}}+{{x}_{2}}\] \[=\frac{d}{\sqrt{2}}+\frac{d}{n}\] \[=\frac{d(n+\sqrt{2})}{n\sqrt{2}}\]You need to login to perform this action.
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