Correct exposure for a photographic print is $10 \, s$ at a distance of $1 \, m$ from a point source of $20 \, cd$. For an equal fogging of the print placed at a distance of $2 \, m$ from a $16 \, cd$ source,the necessary time for exposure is.......$s$.

Shown in the figure is a convergent lens placed inside a cell filled with a liquid. The lens has a focal length of $+20\,cm$ when in air and its material has a refractive index of $1.50$. If the liquid has a refractive index of $1.60$,the focal length of the system is......$cm$.

An optical component and an object $S$ placed along its optic axis are given in Column $I$. The distance between the object and the component can be varied. The properties of images are given in Column $II$. Match all the properties of images from Column $II$ with the appropriate components given in Column $I$.

Column $I$	Column $II$
$A$. Concave Mirror	$(p)$ Real image
$B$. Convex Mirror	$(q)$ Virtual image
$C$. Convex Lens	$(r)$ Magnified image
$D$. Concave Lens	$(s)$ Image at infinity

$A$ 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 $\frac{3 H}{2}\left(1+\frac{\omega^2 H}{2 g}\right)^{-1}$

If the focal length of the objective lens is increased,then the magnifying power of:

If the luminous intensity of a $100 \, W$ unidirectional bulb is $100 \, \text{candela}$, then the total luminous flux emitted from the bulb is ....... $lumen$.