$A$ 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:

The $45^{\circ}-45^{\circ}-90^{\circ}$ prism of height $10 \,cm$ (see image) has a refractive index $\mu = 2$,with a silvered hypotenuse surface. $A$ convex lens of focal length $10 \,cm$ is placed $15 \,cm$ in front of a wall. The system produces a sharp image of point $P$ on the wall. The value of $h$ (in $cm$) is closest to:

In an experiment to determine the focal length of a concave mirror,the object distance is $x$ and the image distance is $y$,both measured from the pole of the mirror. Which of the following graphs correctly represents the relationship between $y$ and $x$?

Define a ray and a beam of light.

Four bulbs,red,green,white and blue (denoted by $R, G, W$ and $B$ respectively) are kept in front of a converging lens (as shown in the figure). The observer sees that the green and blue bulbs are kept to the left of the principal axis,while the red and white bulbs are kept to the right of the principal axis. He also sees that the red and green bulbs are above the principal axis,while the white and blue bulbs are below the principal axis. The screens $S_1$ and $S_2$ are set at appropriate positions for focusing to view the images. Choose the figure that correctly represents the images as seen by the observer.

$A$ 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