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 \(15\) cm. |
2. | Chromatic aberration is minimized. |
3. | Combination behaves like a convergent lens. |
4. | All of these. |
1. | \(75\) | 2. | \(110\) |
3. | \(140\) | 4. | \(25\) |
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 \(\sin ^{-1}\left(\frac{2}{3}\right)\) |
1. | \(-10\) cm | 2. | \(20\) cm |
3. | \(-30\) cm | 4. | \(5\) cm |
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 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. | \(3^{-\frac{1}{2}}\) |
1. | \(32.75\) | 2. | \(327.5\) |
3. | \(0.3275\) | 4. | None of the above |
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. \(3d\)