Question

Match the column if deviation in the column-II is the magnitude of total deviation (between incident ray and finally refracted or reflected ray) to lie between $0^{\circ }$ and ${180}^{\circ }$. Here $n$ represents refractive index of medium.

Column-I	Column -II
	(p) deviation in the light ray is greater than ${90}^{\circ }$
	(q) deviation in the light ray is less than ${90}^{\circ }$
	(r) deviation in the light ray is equal to ${90}^{\circ }$
	(s) Speed of finally reflected or refracted light is same as speed of incident light.

• A. $A-(p,s),B-q,C-(r,s),D-q$
• B. $A-(p,s),B-s,C-(r,s),D-p$
• C. $A-q,B-p,C-r,D-s$
• D. $A-P,B-q,C-s,D-r$

Answer 1

The correct option is A $A-(p,s),B-q,C-(r,s),D-q$

Case $A$ :-
Calculating critical angle for the two mediums :-
$n_1\sin i_c=n_2\sin {90}^{\circ }$
$2\times \sin i_c=1\times 1$
$\sin i_c=\frac{1}{2}$
$\Rightarrow i_c={30}^{\circ }$

If angle of incidence is greater than ${30}^{\circ }$ light ray will get reflected back from interface.

In first case $i>i_c$
$\Rightarrow$ Light will get refelcted back.

Angle of deviation :-
${\delta }_1={180}^{\circ }-2\times {37}^{\circ }$
$={180}^{\circ }-{74}^{\circ }$
$={106}^{\circ }$

In case $B$ :-
$TIR$ will not take place.
Hence, the angle of deviation will be less than ${90}^{\circ }$

In case $C$:-
$i>i_c$
$\therefore$ Angle of deviation is given by:
${\delta }_3={180}^{\circ }-2\times {45}^{\circ }$
$={180}^{\circ }-{90}^{\circ }={90}^{\circ }$


In case $D$ :-
Applying snell`s law for first referaction :-
$n_1\sin i=n_2\sin r$
$1\times \sin \left({90}^{\circ }\right)=2\times \sin \theta$
(Grazing incidence)
$\Rightarrow \sin \theta =\frac{1}{2}$
or, $\theta ={30}^{\circ }$
Now, applying snell`s law at the second interface :-
$2\times \sin {30}^{\circ }=\sqrt{2}\sin i^{\prime }$
$\sin i^{\prime }=\frac{1}{\sqrt{2}}$
or, $i^{\prime }={45}^{\circ }=$ angle of emergence
$\therefore$ Angle of deviation is given by :-
$\delta ={180}^{\circ }-i-e$
$={180}^{\circ }-{90}^{\circ }-{45}^{\circ }={45}^{\circ }$
Here $e=i^{\prime }$)

In case $\left(A\right)$ and $\left(C\right)$ light is reflected back to the same medium.
Therefore, speed of ray will remain same in these two cases.

In the order two cases light goes to other medium after refraction hence, speed of ray will not remain same.

Hence, the correct answer is :-
$A-(p,s),B-q,C-(r,s),D-q$