The following figure shows a beam of light converging at point $$P$$. When a concave lens of focal length $$16 \mathrm{~cm}$$ is introduced in the path of the beam at a place shown by dotted line such that $$O P$$ becomes the axis of the lens, the beam converges at a distance $$x$$ from the lens. The value of $$x$$ will be equal to

A transparent medium shows relation between $$i$$ and $$r$$ as shown. If the speed of light in vacuum is $$c$$, the Brewster angle for the medium is

A point object is moving uniformly towards the pole of a concave mirror of focal length $$25 \mathrm{~cm}$$ along its axis as shown below. The speed of the object is $$1 \mathrm{~ms}^{-1}$$. At $$t=0$$, the distance of the object from the mirror is $$50 \mathrm{~cm}$$. The average velocity of the image formed by the mirror between time $$t=0$$ and $$t=0.25 \mathrm{~s}$$ is

A certain prism is found to produce a minimum deviation of $$38^{\circ}$$. It produce a deviation of $$44^{\circ}$$ when the angle of incidence is either $$42^{\circ}$$ or $$62^{\circ}$$. What is the angle of incidence when it is undergoing minimum deviation?