Two plane mirrors of length $L$ are separated by a distance $L$,and a man $M_2$ is standing at a distance $L$ from the connecting line of the mirrors,as shown in the figure. $A$ man $M_1$ is walking in a straight line at a distance $2L$ parallel to the mirrors at a speed $u$. Then,the man $M_2$ at $O$ will be able to see the image of $M_1$ for a total time of:

If the polarising angle of a piece of glass for green light is $54.74^o$,then the angle of minimum deviation for an equilateral prism made of the same glass is......$^o$ (Given $\tan 54.74^o = 1.414$)

$A$ satisfactory photographic print is obtained when the exposure time is $10 \, s$ at a distance of $2 \, m$ from a $60 \, cd$ lamp. The time of exposure required for the same quality print at a distance of $4 \, m$ from a $120 \, cd$ lamp is $... \, s$.

$A$ 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:

List-$I$	List-$II$
$P$. $e \rightarrow f$	$1$. $\mu_1 > \sqrt{2} \mu_2$
$Q$. $e \rightarrow g$	$2$. $\mu_2 > \mu_1$ and $\mu_2 > \mu_3$
$R$. $e \rightarrow h$	$3$. $\mu_1 = \mu_2$
$S$. $e \rightarrow i$	$4$. $\mu_2 < \mu_1 < \sqrt{2} \mu_2$ and $\mu_2 > \mu_3$

Codes: $P \quad Q \quad R \quad S$

$A$ concave mirror of radius of curvature $h$ is placed at the bottom of a tank containing a liquid of refractive index $\mu$ up to a depth $d$. An object $P$ is placed at a height $h$ above the bottom of the mirror. Outside the liquid,an observer $O$ views the object and its image in the mirror. The apparent distance between these two will be

Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams.