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?

When a pin is moved along the principal axis of a small concave mirror,the image position coincides with the object at a point $0.5\, m$ from the mirror. If the mirror is placed at a depth of $0.2\, m$ in a transparent liquid,the same phenomenon occurs when the pin is placed $0.4\, m$ from the mirror. The refractive index of the liquid is

$A$ lamp is hanging along the axis of a circular table of radius $r$. At what height should the lamp be placed above the table,so that the illuminance at the edge of the table is $\frac{1}{8}$ of that at its center?

$A$ student measures the focal length of a convex lens by obtaining an image of an object pin at a distance '$v$' from the lens,where the object pin is at a distance '$u$' from the lens. What will the graph between '$u$' and '$v$' look like?

An electric lamp is fixed at the ceiling of a circular tunnel as shown in the figure. What is the ratio of the intensities of light at base $A$ and a point $B$ on the wall?

$A$ concave mirror of radius of curvature $h$ is placed at the bottom of a tank containing a liquid of refractive index $\mu$ up to a depth $d$. An object $P$ is placed at a height $h$ above the bottom of the mirror. Outside the liquid,an observer $O$ views the object and its image in the mirror. The apparent distance between these two will be