$A$ good photographic print is obtained at a distance of $20 \,cm$ with an exposure time of $2 \,s$. What will be the exposure time required to get an equally good result at a distance of $40 \,cm$?

Match List $I$ with List $II$ and select the correct answer using the codes given below the lists:

List $I$ (Position of the object)	List $II$ (Magnification)
$(I)$ An object is placed at focus before a convex mirror	$(A)$ Magnification is $-\infty$
$(II)$ An object is placed at centre of curvature before a concave mirror	$(B)$ Magnification is $0.5$
$(III)$ An object is placed at focus before a concave mirror	$(C)$ Magnification is $+1$
$(IV)$ An object is placed at centre of curvature before a convex mirror	$(D)$ Magnification is $-1$
	$(E)$ Magnification is $0.33$

$A$ solid hemisphere of refractive index $\mu_1 = 3/2$ and radius $R = 20\ cm$ is placed as shown in the figure. Another special cylindrical glass of refractive index $\mu_2$,radius $R$,and thickness $t = 2R/3$ is placed adjacent to the flat surface of the solid hemisphere. There is a very small luminous spot at $P$ just inside the solid hemisphere,and the $MN$ surface of the special glass is silvered. Considering only paraxial rays,if the final image of point $P$ for an observer to the left of the hemisphere is at the center $C$ of the hemisphere,find the refractive index $\mu_2$ of the special glass.

$A$ concave mirror is placed on a horizontal table,with its axis directed vertically upwards. Let $O$ be the pole of the mirror and $C$ its centre of curvature. $A$ point object is placed at $C$. It has a real image,also located at $C$ (a condition called auto-collimation). If the mirror is now filled with water,the image will be:

The inverse square law for illuminance is valid for:

Which of the following statements is correct?