A thin rod of length \(\frac{f}{3}\) lies along the axis of a concave mirror of focal length \(f\). One end of its magnified, real image touches an end of the rod. The length of the image is:
1. \(f\)
2. \(\frac{f}{2}\)
3. \(2f\)
4. \(\frac{f}{4}\)
A thin equiconvex lens of power P is cut into three parts A, B, and C as shown in the figure. If P1, P2, and P3 are powers of the three parts respectively, then:
1. | \(P_1=P_2=P_3\) | 2. | \(P_1>P_2=P_3\) |
3. | \(P_1<P_2=P_3\) | 4. | \(P_2=P_3=2P_1\) |
A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is:
1. d/2
2. d
3. 2d
4. 3d
The focal length of the objective lens and the eye lens is 4 mm and 25 mm respectively in a compound microscope. The distance between objective and eyepiece lens is 16 cm. Find its magnifying power for relaxed eye position:
1. | 32.75 |
2. | 327.5 |
3. | 0.3275 |
4. | None of the above |
A medium shows relation between i and r as shown. If the speed of light in the medium is nc then the value of n is:
1. 1.5
2. 2
3. 2–1
4. 3–1/2
In an astronomical telescope in normal adjustment a straight black line of length \(L\) is drawn on inside part of the objective lens. The eye-piece forms a real image of this line. The length of this image is \(l\). The magnification of the telescope is:
1. \(\frac{L}{l+1}\)
2. \(\frac{L}{l-1}\)
3. \(\frac{L+1}{L-1}\)
4. \(\frac{L}{l}\)
For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:
1. | lies between\(\sqrt{2} \text { and } 1 \text {. }\) |
2. | lies between 2 and \(\sqrt{2} \) |
3. | is less than 1. |
4. | is greater than 2. |
A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point \(15~\mathrm{cm}\) from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is:
1. | -10 cm | 2. | 20 cm |
3. | -30 cm | 4. | 5 cm |
The speed of light in media and is and respectively. A ray of light enters from medium to at an incidence angle i. If the ray suffers total internal reflection, the value of i is:
1. | equal to \(\sin ^{-1}\left(\frac{2}{3}\right)\) |
2. | equal to or less than \(\sin ^{-1}\left(\frac{3}{5}\right)\) |
3. | equal to or greater than \(\sin ^{-1}\left(\frac{3}{4}\right)\) |
4. | less than \(\sin ^{-1}\left(\frac{2}{3}\right)\) |
A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the sun is \(1.39\times 10^9~\text{m}\) and its mean distance from the earth is . What is the diameter of the sun's image on the paper?
1. \(
9.2 \times 10^{-4} \mathrm{~m}
\)
2. \(6.5 \times 10^{-4} \mathrm{~m}
\)
3. \(6.5 \times 10^{-5} \mathrm{~m}
\)
4. \( 12.4 \times 10^{-4} \mathrm{~m}\)