For a candle of $40$ power,the exposure time required for a photographic print at a distance of $0.6 \, m$ is $20 \, s$. What will be the exposure time required for the same print at a distance of $1.2 \, m$ using a candle of $20$ power?

Two plane mirrors of length $L$ are separated by a distance $L$,and a man $M_2$ is standing at a distance $L$ from the connecting line of the mirrors,as shown in the figure. $A$ man $M_1$ is walking in a straight line at a distance $2L$ parallel to the mirrors at a speed $u$. Then,the man $M_2$ at $O$ will be able to see the image of $M_1$ for a total time of:

The photograph of a house occupies an area of $1.75 \; cm^2$ on a $35 \; mm$ slide. The slide is projected onto a screen,and the area of the house on the screen is $1.55 \; m^2$. What is the linear magnification of the projector-screen arrangement?

$A$ small object is placed $50 \ cm$ to the left of a thin convex lens of focal length $30 \ cm$. $A$ convex spherical mirror of radius of curvature $100 \ cm$ is placed to the right of the lens at a distance of $50 \ cm$. The mirror is tilted such that the axis of the mirror is at an angle $\theta=30^{\circ}$ to the axis of the lens,as shown in the figure. If the origin of the coordinate system is taken to be at the centre of the lens,the coordinates (in $cm$) of the point $(x, y)$ at which the image is formed are

The exposure time of a camera lens at the $f/2.8$ setting is $1/200$ second. The correct time of exposure at $f/5.6$ is......$sec$

$A$ ray of light strikes a plane mirror at an angle of incidence $45^o$ as shown in the figure. After reflection,the ray passes through a prism of refractive index $1.5$,whose apex angle is $4^o$. The angle through which the mirror should be rotated if the total deviation of the ray is to be $90^o$ is