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. \(34\)
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 |
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 |
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 μ_{1} and μ_{2} and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is:
1. R/2(μ_{1 + }μ_{2})
2. R/2(μ_{1 - }μ_{2})
3. R/(μ_{1 - }μ_{2})
4. 2R/(μ_{2 }- μ_{1})
An astronomical telescope has an objective and eyepiece of focal lengths \(40\) cm and \(4\) cm respectively. To view an object \(200\) cm away from the objective, the lenses must be separated by a distance:
1. \(46.0\) cm
2. \(50.0\) cm
3. \(54.0\) cm
4. \(37.3\) cm
Match the corresponding entries of Column-1 with Column-2. (Where \(m\) is the magnification produced by the mirror)
Column-1 | Column-2 |
A. \(m= -2\) | I. convex mirror |
B. \(m= -\frac{1}{2}\) | II. concave mirror |
C. \(m= +2\) | III. real Image |
D. \(m= +\frac{1}{2}\) | IV. virtual Image |
A | B | C | D | |
1. | I & III | I & IV | I & II | III & IV |
2. | I & IV | II & III | II & IV | II & III |
3. | III & IV | II & IV | II & III | I & IV |
4. | II & III | II & III | II & IV | I & IV |
A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels up, to the surface of the liquid and moves along its surface (see figure).
How fast is the light traveling in the liquid?
1. | \(1.8 \times 10^8 \mathrm{~m} / \mathrm{s} \) | 2. | \(2.4 \times 10^8 \mathrm{~m} / \mathrm{s} \) |
3. | \(3.0 \times 10^8 \mathrm{~m} / \mathrm{s} \) | 4. | \(1.2 \times 10^8 \mathrm{~m} / \mathrm{s}\) |
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:
1. \(\theta = 49^{\circ}\)$$
2. \(\theta = 90^{\circ}\)$$
3. \(\theta = 98^{\circ}\)$\mathrm{}$
4. \(\theta = 24\frac{1}{2}^{\circ}\)$$
A glass sphere $\left(\mu =\frac{3}{2}\right)$ of radius 12 cm has a small mark at a distance of 3 cm from its centre. Where will this mark appear when it is viewed from the side nearest to the mark along the line joining the centre and the mark?
1. | 8 cm inside the sphere | 2. | 12 cm inside the sphere |
3. | 4 cm inside the sphere | 4. | 3 cm inside the sphere |