What is an image?

Amount of light entering into the camera depends upon

$A$ 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.

For the refraction of light through a prism,which of the following statements is correct?

$A$ ray of sunlight enters a spherical water droplet $(n = 4/3)$ at an angle of incidence $53^o$ measured with respect to the normal to the surface. It is reflected from the back surface of the droplet and re-enters into air. The angle between the incoming and outgoing ray is $.......^o$ [Take $\sin \,53^o = 0.8$]

$A$ point source of light is $60\, cm$ from a screen and is kept at the focus of a concave mirror which reflects light on the screen. The focal length of the mirror is $20\, cm$. The ratio of average intensities of the illumination on the screen when the mirror is present and when the mirror is removed is: (in $: 1$)