Question

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

	Column-I		Column-II
(P)		(1)	Deviation in the light ray is greater than ${90}^0$
(Q)		(2)	Deviation in the light ray is less than ${90}^0$
(R)		(3)	Deviation in the light ray is ${90}^0$
(S)		(4)	Speed of finally reflected or refracted light is same as that of incident light

• A. P - 4, Q - 2, R - 1, S - 3
• B. P - 1, Q - 2, R - 4, S - 2
• C. P - 3, Q - 1, R - 4, S - 2
• D. P - 2, Q - 4, R - 1, S - 3

Answer 1

The correct option is B P - 1, Q - 2, R - 4, S - 2

The critical angle, $C=si{n}^{-1}\frac{1}{\mu }$
When incident angle is greater than critical angle, TIR will happen.
Now,
$C=si{n}^{-1}\frac{1}{2/1}={30}^0$
For Case-P
$i={37}^0$ $\Rightarrow i>\delta$
So reflection happens.
Therefore, $\delta =\pi -2\left(37\right)={104}^0$
Thus the deviation in the light ray is greater than ${90}^0$
For Case-Q
$i={25}^0$ $\Rightarrow i<\delta$
So refraction happens.
Thus, the deviation in the light ray is less than ${90}^0$
For case-R
$i={45}^0$ $\Rightarrow i>\delta$
So reflection happens.
so $\delta =\pi -2\left(\frac{\pi }{4}\right)={90}^0$

For case-S
For prism, as incident rays are grazing, therefore $i\approx {90}^0$
By applying Snell's law for prism,
$r_1={30}^0\text{and}{r}_2=A-r_1={30}^0$
Emergence angle, $i^{\prime \prime }={45}^0$
Therefore, $\delta =i+i^{\prime \prime }-A=90+45-60={75}^0$
Hence, option (B) matches correctly.