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. \(34\)
1. | \(4~\text{cm}^2 \) | 2. | \(6~\text{cm}^2 \) |
3. | \(16~\text{cm}^2 \) | 4. | \(36~\text{cm}^2 \) |
1. | \(6\) cm | 2. | \(9\) cm |
3. | \(12\) cm | 4. | \(15\) cm |
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 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 surface \(A\) will emerge from the glass through \(B\)?
1. | \(1.5\) | 2. | \(0.5\) |
3. | \(1.3\) | 4. | None of these |
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:
1. | zero | 2. | \(\alpha\) |
3. | \(\sin^{-1}\left(\frac{1}{n}\right)\) | 4. | \(2\sin^{-1}\left(\frac{1}{n}\right)\) |
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 \(10\) 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 \(15\) cm from pole \(P\) as shown. The distance of the final image of \(O\) from \(P\) as viewed from the left is:
1. | \(20\) cm | 2. | \(30\) cm |
3. | \(40\) cm | 4. | \(50\) cm |
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:
1. | \(10\) cm | 2. | \(20\) cm |
3. | \(30\) cm | 4. | Cannot be determined |
1. | 2. | ||
3. | 4. |
1. | \(12~\text{cm}\) | 2. | \(30~\text{cm}\) |
3. | \(50~\text{cm}\) | 4. | \(60~\text{cm}\) |
1. | \(5\) cm/sec towards the mirror |
2. | \(4\) cm/sec towards the mirror |
3. | \(4\) cm/sec away from the mirror |
4. | \(9\) cm/sec away from the mirror |