question_answer

A point source S is placed at the bottom of a transparent block of height \[10\text{ }mm\]and refractive index\[2.72\]. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter \[11.54\text{ }mm\]on the top of the block. The refractive index of the liquid is

A) \[1.21\]

B)        \[130\]

C) \[1.36\]

D)        \[1.42\]

Correct Answer: C

Solution :

\[\sin \,{{i}_{c}}=\frac{r}{\sqrt{{{r}^{2}}+{{h}^{2}}}}\] \[\Rightarrow \,\,\frac{{{n}_{l}}}{{{n}_{B}}}=\frac{r}{\sqrt{{{r}^{2}}+{{h}^{2}}}}\times 2.72\] \[\Rightarrow \,{{n}_{l}}=\frac{r}{\sqrt{{{r}^{2}}+{{h}^{2}}}}\times 2.72=\frac{5.77}{11.54}\times 2.72=1.36\]