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

$A$ bulb of $100 \text{ W}$ is hanging at a height of $1 \text{ m}$ above the centre of a circular table of diameter $4 \text{ m}$. If the intensity at a point on its rim is $I_0$,then the intensity at the centre of the table will be:

Which of the following statements is correct?

If the luminous efficiency of a lamp is $2 \text{ lumen/watt}$ and its luminous intensity is $42 \text{ candela}$,then the power of the lamp is.......$W$

$A$ solid hemisphere of refractive index $\mu_1 = 3/2$ and radius $R = 20\ cm$ is placed as shown in the figure. Another special cylindrical glass of refractive index $\mu_2$,radius $R$,and thickness $t = 2R/3$ is placed adjacent to the flat surface of the solid hemisphere. There is a very small luminous spot at $P$ just inside the solid hemisphere,and the $MN$ surface of the special glass is silvered. Considering only paraxial rays,if the final image of point $P$ for an observer to the left of the hemisphere is at the center $C$ of the hemisphere,find the refractive index $\mu_2$ of the special glass.

$A$ point source of $100$ candela is held $5\,m$ above a sheet of blotting paper which reflects $75\%$ of light incident upon it. The illuminance of the blotting paper is