Q. No.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 \((A)\) 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. \(\frac{d}{2}\)
2. \(d\)
3. \(2d\)
4. \(3d\)
1. \(\frac{d}{2}\)
2. \(d\)
3. \(2d\)
4. \(3d\)
| 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. | \(3^{-\frac{1}{2}}\) |
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. \(\frac{L}{l}+1\)
2. \(\frac{L}{l}-1\)
3. \(\frac{L+1}{l-1}\)
4. \(\frac{L}{l}\)
| 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 \(2\). |
| 1. | \(-10\) cm | 2. | \(20\) cm |
| 3. | \(-30\) cm | 4. | \(5\) cm |
| 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. |
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