In a grease spot photometer,light from a lamp with a dirty chimney is exactly balanced by a point source at a distance of $10 \, cm$ from the grease spot. On cleaning the chimney,the point source is moved by $2 \, cm$ to obtain balance again. The percentage of light absorbed by the dirty chimney is nearly......$\%$

$A$ double convex lens $(R_1 = R_2 = 10\,cm)$ with refractive index $(\mu = 1.5)$ has a focal length equal to the focal length of a concave mirror. The radius of curvature of the concave mirror is.......$cm$.

$A$ glass sphere of refractive index $1.5$ and radius $40\,cm$ has half its hemispherical surface silvered. The point where a parallel beam of light,coming along a diameter,will focus (or appear to) after coming out of the sphere,will be:

$A$ 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:

$A$ small fish,$0.4\,m$ below the surface of a lake,is viewed through a simple converging lens of focal length $3\,m$. The lens is kept at $0.2\,m$ above the water surface such that the fish lies on the optical axis of the lens. The image of the fish seen by the observer will be at $\left( \mu_{water} = \frac{4}{3} \right)$

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: