$A$ double convex lens $(R_1 = R_2 = 10\,cm)$ with refractive index $(\mu = 1.5)$ has a focal length equal to the focal length of a concave mirror. The radius of curvature of the concave mirror is.......$cm$.

The flat bottom of a cylindrical tank is silvered and water $(\mu = 4/3)$ is filled in the tank up to a height $h$. $A$ small bird is hovering at a height $3h$ from the bottom of the tank. When a small hole is opened near the bottom of the tank,the water level falls at the rate of $1\, cm/s$. The bird will perceive that its image's velocity is:

Ray optics is valid when characteristic dimensions are:

$A$ horizontal parallel beam of light passes through a vertical convex lens of focal length $20 \,cm$ and is then reflected by a tilted plane mirror,so that it converges to a point $I$. The distance $P I$ is $10 \,cm$. $M$ is a point at which the axis of the lens intersects the mirror. The distance $P M$ is $10 \,cm$. The angle which the mirror makes with the horizontal is (in $^{\circ}$)

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

$A$ light source is located at $P_1$ as shown in the figure. All sides of the polygon are equal. The intensity of illumination at $P_2$ is $I_0$. What will be the intensity of illumination at $P_3$?