An object approaches a convergent lens from the left of the lens with a uniform speed $$5 \mathrm{~m} / \mathrm{s}$$ and stops at the focus, the image

The refracting angle of prism is $$A$$ and refractive index of material of prism is $$\cot \frac{A}{2}$$. The angle of minimum deviation is $$A$$

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