Q. No.A thin rod of length \(\dfrac{f}{3}\) 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.
\(\dfrac{f}{2}\)
3.
\(2f\)
4.
\(\dfrac{f}{4}\)
A thin equiconvex lens of power \(P\) is cut into three parts \(A,B,\) and \(C\) as shown in the figure. If \(P_1,P_2\) and \(P_3\) 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 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. | \(3^{-\frac{1}{2}}\) |
A person can see clearly objects only when they lie between \(50~\text{cm}\) and \(400~\text{cm}\) from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use will be:
| 1. | \(\text{convex, +2.25 diopter}\) | 2. | \(\text{concave, -0.25 diopter}\) |
| 3. | \(\text{concave, -0.2 diopter}\) | 4. | \(\text{convex, +0.5 diopter}\) |
| 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 \(1.5\times 10^{11}~\text{m}.\) What is the diameter of the sun's image on the paper?
1. \( 9.2 \times 10^{-4}~\text{m} \)
2. \(6.5 \times 10^{-4}~\text{m} \)
3. \(6.5 \times 10^{-5}~\text{m} \)
4. \( 12.4 \times 10^{-4}~\text{m} \)
| 1. | the effective focal length is \(15~\text{cm}.\) |
| 2. | the chromatic aberration is minimized. |
| 3. | the combination behaves like a convergent lens. |
| 4. | all of these. |
| 1. | \(\frac{\sqrt{3}}{2} \) | 2. | \(1.5 \) |
| 3. | \(1.732 \) | 4. | \( 2\) |
An object is placed \(20~\text{cm}\) in front of a concave mirror of a radius of curvature \(10~\text{cm}.\) The position of the image from the pole of the mirror is:
1. \(7.67~\text{cm}\)
2. \(6.67~\text{cm}\)
3. \(8.67~\text{cm}\)
4. \(9.67~\text{cm}\)
If \(C_1,~C_2 ~\mathrm{and}~C_3\) are the critical angle of glass-air interface for red, violet and yellow color, then:
| 1. | \(C_3>C_2>C_1\) | 2. | \(C_1>C_2>C_3\) |
| 3. | \(C_1=C_2=C_3\) | 4. | \(C_1>C_3>C_2\) |
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