$A$ 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 $; cm$)?

$A$ 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:

$A$ glass sphere of refractive index $1.5$ and radius $40\,cm$ has half its hemispherical surface silvered. The point where a parallel beam of light,coming along a diameter,will focus (or appear to) after coming out of the sphere,will be:

For a concave mirror, if a virtual image is formed, the graph between $m$ and $u$ is of the form:

In the figure shown,if the object $O$ moves towards the plane mirror $M_1$,then the image $I$ (which is formed after successive reflections from $M_1$ and $M_2$ respectively) will move:

$A$ light source is located at $P_1$ as shown in the figure. All sides of the polygon are equal. The intensity of illumination at $P_2$ is $I_0$. What will be the intensity of illumination at $P_3$?