$A$ convex mirror and a concave mirror of radius $10\; cm$ each are placed $15\; cm$ apart facing each other. An object is placed midway between them. If the reflection first takes place in the concave mirror and then in the convex mirror,the position of the final image is:

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

An object is placed on the principal axis of a convex lens of focal length $10\,cm$ as shown. $A$ plane mirror is placed on the other side of the lens at a distance of $20\,cm$. The final image produced by the plane mirror is $5\,cm$ behind the mirror. The distance of the object from the lens is $............cm$.

$A$ lamp is hanging at a height of $4\,m$ above a table. The lamp is lowered by $1\,m$. The percentage increase in illuminance will be.....$\%$

In a laboratory,a material is created with a negative refractive index. $A$ light ray enters from medium $1$ into this material (medium $2$). Which of the following diagrams correctly represents the path of the ray?

Four bulbs,red,green,white and blue (denoted by $R, G, W$ and $B$ respectively) are kept in front of a converging lens (as shown in the figure). The observer sees that the green and blue bulbs are kept to the left of the principal axis,while the red and white bulbs are kept to the right of the principal axis. He also sees that the red and green bulbs are above the principal axis,while the white and blue bulbs are below the principal axis. The screens $S_1$ and $S_2$ are set at appropriate positions for focusing to view the images. Choose the figure that correctly represents the images as seen by the observer.