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......$\%$

$A$ 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:

The object distance $u$,the image distance $v$,and the magnification $m$ in a lens follow certain linear relations. These are:

Which has more luminous efficiency?

The figure shows a ray incident at an angle $i = \pi / 3$. The plot shows the variation of $|r - i|$ versus $k = \frac{\mu_1}{\mu_2}$,where $r$ is the angle of refraction. Based on the graph,which of the following statements is correct?

$A$ 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.......$cm$.