A spherical glass is attached to a rigid wall as shown in the figure. An observer located at point $O$ is looking at a point $A$ on the wall. The refractive index of the glass is 1.5 and that of air is 1.0 . The distances are $O A=8 \mathrm{~cm}$, $X A=3 \mathrm{~cm}$. If the radius of curvature of spherical glass surface is $R=5 \mathrm{~cm}$, then the apparent distance of $A$ from observer $O$ is

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