Question

Match the proper entries from column- $2$ to column- 1 using the codes given below in the columns. Deviation in the Column-II is the magnitude of total deviation (between incident ray and finally refracted or reflected ray) which lies between $0^{\circ }$ and ${180}^{\circ }.$ Here $n$ represents refractive index of medium.

Column-I	Column-II
(p)	(1) deviation in the light ray is greater than ${90}^{\circ }$
(q)	(2) deviation in the light ray is less than ${60}^{\circ }$
(r)	(3) deviation in the light ray is greater than ${60}^{\circ }$ but less than ${90}^0$
(s)	(4) Speed of light remains same after falling on the boundary of two mediums.

• A. p-3,4; q-1,4; r-4; s-2
• B. p-1,3,4; q-2; r-3,4; s-2,3
• C. p-4,2; q-2,4; r-1,4; s-3
• D. p-1,4; q-3; r-3,4; s-3

Answer 1

The correct option is B p-1,3,4; q-2; r-3,4; s-2,3

$C=si{n}^{-1}\left(\frac{1}{2/1}\right)=30$

for $i={37}^o,$ incident ray will undergo TIR so, $\delta =\pi -2\left({37}^0\right)={104}^0$

$i={25}^o$, Refraction $\delta <\frac{\pi }{2}-C$
$i={45}^{\circ },$ incident ray will undergo $TIR$
$$\text{so},\delta =\pi -2\left(\frac{\pi }{4}\right)={90}^{\circ }$$

By applying snells law for prism:
$$\begin{array}{cc}i=90& \\ r_1=30,r_2=30& \\ e=45& \\ \delta =90+45& -60={75}^{\circ }\end{array}$$