Write the names of instruments developed by the use of properties of reflection and refraction of mirrors,lenses,and prisms.

Four bulbs,red,green,white and blue (denoted by $R, G, W$ and $B$ respectively) are kept in front of a converging lens (as shown in the figure). The observer sees that the green and blue bulbs are kept to the left of the principal axis,while the red and white bulbs are kept to the right of the principal axis. He also sees that the red and green bulbs are above the principal axis,while the white and blue bulbs are below the principal axis. The screens $S_1$ and $S_2$ are set at appropriate positions for focusing to view the images. Choose the figure that correctly represents the images as seen by the observer.

Two light sources with equal luminous intensity are placed at a distance of $1.2\, m$ from each other. Where should a screen be placed between them such that the illuminance on one of its faces is four times that on the other face?

$A$ lamp is hanging at a height of $40\, cm$ from the center of a table. If its height is increased by $10\, cm$,the illuminance on the table will decrease by what percentage?

$A$ 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.

Which of the following form$(s)$ a virtual and erect image for all positions of the object?