Question

Match the proper entries from column- II to column-I using the codes given below in the columns. Deviation given in 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 or equal to ${90}^0$
(s)	(4) speed of light remains same after falling on the boundary of two mediums.

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

Answer 1

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

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

For $i={37}^o,$ incident ray will undergo TIR.
So $\delta =\pi -2\left({37}^0\right)={106}^0$

For $i={25}^o$, incident ray will undergo refraction.
$\delta <\frac{\pi }{2}-C$
$\delta <{60}^{\circ }$

For $i={45}^{\circ }$, incident ray will undergo TIR
So $\delta =\pi -2\left(\frac{\pi }{4}\right)={90}^{\circ }$

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