Five lumen/watt is the luminous efficiency of a lamp and its luminous intensity is $35$ candela. The power of the lamp is.......$W$

$A$ ray of light moving along the vector $\vec{v} = -\hat{i} - 2\hat{j}$ undergoes refraction at an interface of two media,which is the $x-z$ plane. The refractive index for $y > 0$ is $\mu_1 = 2$,while for $y < 0$,it is $\mu_2 = \sqrt{5}/2$. Find the unit vector along which the refracted ray moves.

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

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

$A$ concave mirror is placed at the bottom of an empty tank with its face upwards and axis vertical. When sunlight falls normally on the mirror,it is focused at a distance of $32 \, cm$ from the mirror. If the tank is filled with water $\left( \mu = \frac{4}{3} \right)$ up to a height of $20 \, cm$,then the sunlight will now be focused at:

For a concave mirror, if a virtual image is formed, the graph between $m$ and $u$ is of the form: