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 \(B?\)

               

1.	\(1.5\)	2.	\(0.5\)
3.	\(1.3\)	4.	None of these

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:
          
1. \(20~\text{cm}\)
2. \(30~\text{cm}\)
3. \(40~\text{cm}\)
4. \(50~\text{cm}\)

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:

Two plane mirrors, \(A\) and \(B\) are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of \(30^\circ\) at a point just inside one end of \(A.\) The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (excluding the first one) before it emerges out is:
   
1. \(28\)                     
2. \(30\)
3. \(32\)         
4. \(34\)

In the figure shown the angle made by the light ray with the normal in the medium of refractive index \(\sqrt{2}\) is:
                   
1. \(30^{\circ}\)$$

2. \(60^{\circ}\)$$

3. \(90^{\circ}\)$$

4. None of these

A fish is a little away below the surface of a lake. If the critical angle is \(49^{\circ},\) then the fish could see things above the water surface within an angular range of \(\theta^{\circ}\) where: