A light ray travels from a medium with refractive index $n_1$ to another medium of refractive index $n_2$. If $n_1=2$ and $n_2=\sqrt{3}$, then find the critical angle.

A convex lens focusses an object 20 cm from it on a screen placed 5 cm away from it. A glass plate (refractive index $=7 / 5$ ) of thickness 1.4 cm is inserted between the lens and the screen. What is the distance of the object from the lens, so that its image is again focused on the screen?

A lens is made of glass having an index of refraction 1.5 . One side of the lens is flat and the other side is convex with a radius $R$. If an object is placed 60 cm , towards the convex side of the lens, the image is formed at

A short straight object of length $l$ lies along the central axis of a spherical concave mirror, at a distance $X$ from the mirror. The focal length of the mirror is $F$. If the length of the image in the mirror is $l^{\prime}$, then ratio $\left(\frac{l^{\prime}}{l}\right)$ is (assume, $l \ll X$ and $l \ll F$ )