$A$ diverging lens of focal length $10 \, cm$ is placed $10 \, cm$ in front of a plane mirror as shown in the figure. Light from a very far away source falls on the lens. The final image is at a distance

$A$ lamp is hanging $1 \, m$ above the center of a circular table of diameter $1 \, m$. The ratio of illuminances at the center and the edge is:

The dispersive power of the material of a lens of focal length $20 \; cm$ is $0.08$. The longitudinal chromatic aberration of the lens is ...... $cm$.

Shown in the figure is a convergent lens placed inside a cell filled with a liquid. The lens has a focal length of $+20\,cm$ when in air and its material has a refractive index of $1.50$. If the liquid has a refractive index of $1.60$,the focal length of the system is......$cm$.

$A$ fish in an aquarium,$30 \, cm$ deep in water,can see a light bulb kept $50 \, cm$ above the surface of water. The fish can also see the image of this bulb in the reflecting bottom surface of the aquarium. The total depth of water is $60 \, cm$. Then the apparent distance between the two images seen by the fish is $(\mu_w = 4/3)$.

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