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?

Discuss the sign convention of distances for reflection by a spherical mirror and refraction by a spherical lens.

$A$ lamp rated at $100 \, cd$ hangs over the middle of a round table with diameter $3 \, m$ at a height of $2 \, m$. It is replaced by a lamp of $25 \, cd$ and the distance to the table is changed so that the illumination at the centre of the table remains as before. The illumination at the edge of the table becomes $X$ times the original. Then $X$ is

$A$ cubic block of glass with refractive index $n_1$ is in contact with the surface of water with refractive index $n_2$. $A$ ray of light is incident on the vertical face of the block (see figure). After refraction,total internal reflection at the base,and refraction at the opposite vertical face,the ray emerges at an angle $\theta$. The value of $\theta$ is given by:

$A$ point source $S$ is placed at a distance of $15 \; cm$ from a converging lens of focal length $10 \; cm$. Where should a concave mirror of focal length $12 \; cm$ be placed so that a real image is formed on the object itself (in $; cm$)?

Find the luminous intensity of the sun if it produces the same illuminance on the earth as produced by a bulb of $10000 \, cd$ at a distance of $0.3 \, m$. The distance between the sun and the earth is $1.5 \times 10^{11} \, m$.