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 \(15\) 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. | \(-10\) 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 person can see clearly objects only when they lie between 50 cm and 400 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. | Convex, +2.25 D |
2. | Concave, - 0.25 D |
3. | Concave, - 0.2 D |
4. | Convex, + 0.15 D |
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 |