Discussion Forum

1)

A point source S is placed at the bottom of the transparent block of height 10 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 mm on the top of the block . The refractive index of the liquid is 

Answer:

Option C

Explanation:

At point Q angle of incidence is critical angle  $\theta_{C}$   , where

$\sin\theta_{C}=\frac{\mu_{1}}{\mu_{block}}$

 In   $\triangle PQS,$      $\sin \theta_{C}=\frac{r}{\sqrt{r^{2}+h^{2}}}$

 $\therefore$     $\frac{\mu_{l}}{\mu_{block}}=\frac{r}{\sqrt{r^{2}+h^{2}}}$

$\Rightarrow$        $\mu_{l}=\frac{r}{\sqrt{r^{2}+h^{2}}}\times2.72$

   $=\frac{5.77}{11.54}\times2.72=1.36$