Assertion: By roughening the surface of a glass sheet,its transparency can be reduced.
Reason: Glass sheet with a rough surface absorbs more light.

An object is placed $20 \, cm$ in front of a convex mirror. $A$ plane mirror is also placed such that the virtual images formed by both mirrors coincide. If the plane mirror is placed $15 \, cm$ from the object,find the focal length of the convex mirror in $cm$.

$A$ lamp is hanging along the axis of a circular table of radius $r$. At what height should the lamp be placed above the table,so that the illuminance at the edge of the table is $\frac{1}{8}$ of that at its center?

If two mirrors are placed side-by-side on a wall and one is placed on the ceiling,how many images will be formed?

In an experiment for the determination of focal length of a convex mirror,a convex lens of focal length $20 \ cm$ is placed on an optical bench and an object pin is placed at a distance $30 \ cm$ from the lens. When a convex mirror is introduced in between the lens and the real and inverted image of the object,the final image of the object $O$ is formed at $O$ itself. If the distance between the lens and the mirror is $10 \ cm$,then the focal length of the mirror is.......$cm$

$A$ light ray is incident on the surface of a sphere of refractive index $n$ at an angle of incidence $\theta_0$. The ray partially refracts into the sphere with angle of refraction $\phi_0$ and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is $\alpha$. Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option.

$List-I$	$List-II$
$(P)$ If $n=2$ and $\alpha=180^{\circ}$,then all the possible values of $\theta_0$ will be	$(1)$ $30^{\circ}$ and $0^{\circ}$
$(Q)$ If $n=\sqrt{3}$ and $\alpha=180^{\circ}$,then all the possible values of $\theta_0$ will be	$(2)$ $60^{\circ}$ and $0^{\circ}$
$(R)$ If $n=\sqrt{3}$ and $\alpha=180^{\circ}$,then all the possible values of $\phi_0$ will be	$(3)$ $45^{\circ}$ and $0^{\circ}$
$(S)$ If $n=\sqrt{2}$ and $\theta_0=45^{\circ}$,then all the possible values of $\alpha$ will be	$(4)$ $150^{\circ}$
	$(5)$ $0^{\circ}$