Two lamps of luminous intensity of $8 \, Cd$ and $32 \, Cd$ respectively are lying at a distance of $1.2 \, m$ from each other. Where should a screen be placed between the two lamps such that its two faces are equally illuminated due to the two sources?

$A$ light ray is incident,at an incident angle $\theta_{1}$,on the system of two plane mirrors $M_{1}$ and $M_{2}$ having an inclination angle $75^{\circ}$ between them (as shown in figure). After reflecting from mirror $M_{1}$,it gets reflected back by the mirror $M_{2}$ with an angle of reflection $30^{\circ}$. The total deviation of the ray will be $\dots$ degree.

$A$ $2\,m$ long scale with a least count of $0.2\,cm$ is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at $80\,cm$ mark and $1\,m$ mark, respectively. The image of the object pin on the other side of the lens coincides with the image pin that is kept at $180\,cm$ mark. The $\%$ error in the estimation of focal length is

$A$ convex mirror and a concave mirror of radius $10\; cm$ each are placed $15\; cm$ apart facing each other. An object is placed midway between them. If the reflection first takes place in the concave mirror and then in the convex mirror,the position of the final image is:

$A$ point object is placed at a distance of $60\, cm$ from a convex lens of focal length $30\, cm$. If a plane mirror is placed perpendicular to the principal axis of the lens at a distance of $40\, cm$ from it,the final image is formed at a distance of:

$A$ convex mirror of focal length $15 \ cm$ and a concave mirror of focal length $10 \ cm$ are placed facing each other at a distance of $40 \ cm$ apart. $A$ point object is placed between the mirrors on their common axis at a distance of $15 \ cm$ from the concave mirror. The position of the image formed by reflection at the convex mirror will be at a distance of ..... $cm$ from it.