Question

A right angled prism of refractive index ${\mu }_1$ is placed in a rectangular block of refractive index ${\mu }_2$, which is surrounded by a medium of refractive index ${\mu }_3$, as shown in the figure. A ray of light e' enters the rectangular block at normal incidence. Depending upon the relationships between ${\mu }_1,{\mu }_2$ and ${\mu }_3$, it takes one of the four possible paths ` ef', ` 'eg', ` eh', or ` ei'
Match the paths in List I with conditions of refractive indices in List II and select the correct answer using the codes given below the lists:

Answer 1

$A.\to \left(2\right)$ ; $B.\to \left(3\right)$ ;
$C.\to \left(4\right)$ ; $D.\to \left(1\right)$

$A.{\mu }_2>{\mu }_1\dots$ (towards normal)
${\mu }_2>{\mu }_3\dots$ (away from normal)
$B.{\mu }_1={\mu }_2\dots$ (No change in path)
$\angle i=0=>\angle r=0$ on the block.
$C.{\mu }_1>{\mu }_2\dots$ (Away from the normal)
${\mu }_2>{\mu }_3\dots$ (Away from the normal)
${\mu }_1\times \frac{1}{\sqrt{2}}={\mu }_2$ sinr $\Rightarrow sinr=\frac{{\mu }_1}{\sqrt{2}{\mu }_2}$ Since sinr
$<1=>{\mu }_1<\sqrt{2}{\mu }_2$
$D$. For TIR:
${45}^0>C=>\sin {45}^0>\sin C=>\frac{1}{\sqrt{2}}>\frac{{\mu }_2}{{\mu }_1}=>{\mu }_1>\sqrt{2}{\mu }_2$