The refracting angle of a prism is \(A\), and refractive index of the material of the prism is \(\cot{\left(\frac{A}{2}\right)}\). The angle of minimum deviation is:
1. \(180^{\circ}-3A\)
2. \(180^{\circ}-2A\)
3. \(90^{\circ}-A\)
4. \(180^{\circ}+2A\)

A plane-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices \(\mu_1\) and \(\mu_2\) and \(R\) is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is:

The distance between a convex lens and a plane mirror is \(10\) cm. The parallel rays incident on the convex lens, after reflection from the mirror form image at the optical centre of the lens. Focal length of the lens will be:

The slab of a refractive index material equal to \(2\) shown in the figure has a curved surface \(APB\) of a radius of curvature of \(10~\text{cm}\) and a plane surface \(CD.\) On the left of \(APB\) is air and on the right of \(CD\) is water with refractive indices as given in the figure. An object \(O\) is placed at a distance of \(15~\text{cm}\) from the pole \(P\) as shown. The distance of the final image of \(O\) from \(P\) as viewed from the left is:
          

A diverging beam of light from a point source \(S\) having divergence angle \(\alpha,\) falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is \(t\) and the refractive index \(n\), then the divergence angle of the emergent beam is:
   

A rod of glass \((\mu = 1.5)\) and of the square cross-section is bent into the shape as shown. A parallel beam of light falls on the plane's flat surface \(A\) as shown in the figure. If \(d\) is the width of a side and \(R\) is the radius of a circular arc then for what maximum value of \(\frac{d}{R},\) light entering the glass slab through the surface \(A\) will emerge from the glass through \(B?\)