$A$ hemispherical glass body of radius $10\, cm$ and refractive index $1.5$ is silvered on its curved surface. $A$ small air bubble is $6\, cm$ below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen:

As shown in the figure, a parallel beam of light is incident on the upper part of a prism of angle $1.8^{\circ}$ and material of refractive index $1.5$. The light emerging from the prism falls on a concave mirror of radius of curvature $40 \,cm$. The distance of the point from the principal axis of the mirror where the light rays are focused after reflection from the mirror is:

$A$ movie projector forms an image $3.5 \ m$ long of an object $35 \ mm$ long. Supposing there is negligible absorption of light by the aperture,what is the ratio of the illuminance on the slide to the illuminance on the screen?

$A$ beaker of radius $r$ is filled with water (refractive index $\frac{4}{3}$) up to a height $H$ as shown in the figure. The beaker is kept on a horizontal table rotating with angular speed $\omega$. This makes the water surface curved so that the difference in the height of the water level at the center and at the circumference of the beaker is $h$ $(h \ll H, h \ll r)$,as shown in the figure. Take this surface to be approximately spherical with a radius of curvature $R$. Which of the following is/are correct? ($g$ is the acceleration due to gravity)
$(A)$ $R=\frac{h^2+r^2}{2 h}$
$(B)$ $R=\frac{r^2}{2 h}$
$(C)$ Apparent depth of the bottom of the beaker is close to $\frac{3 H}{4}\left(1+\frac{\omega^2 H}{4 g}\right)^{-1}$
$(D)$ Apparent depth of the bottom of the beaker is close to $\frac{3 H}{2}\left(1+\frac{\omega^2 H}{2 g}\right)^{-1}$

The inverse square law for illuminance is valid for:

$A$ 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 $sin \,53^o = 0.8$]