Q. No.A thin convex lens made from crown glass \(\left(\mu=\frac{3}{2}\right) \) has focal length \(f\). When it is measured in two different liquids having refractive indices \(\frac{4}{3}\) and \(\frac{5}{3}\), it has the focal lengths \(f_1\) and \(f_2\) respectively. The correct relation between the focal lengths is:
| 1. | \(f_1>f\) and \(f_2\) becomes negative |
| 2. | \(f_2>f\) and \(f_1\) becomes negative |
| 3. | \(f_1\) and \(f_2\) becomes negative |
| 4. | \(f_1=f_2<f\) |
A green light is an incident from the water to the air-water interface at the critical angle \((\theta)\). Select the correct statement:
| 1. | The spectrum of visible light whose frequency is less than that of green light will come out to the air medium. |
| 2. | The spectrum of visible light whose frequency is more than that of green light will come out to the air medium. |
| 3. | The entire spectrum of visible light will come out of the water at various angles to the normal. |
| 4. | The entire spectrum of visible light will come out of the water at an angle of \(90^\circ\) to the normal. |
Monochromatic light is incident on a glass prism of angle \(A\). If the refractive index of the material of the prism is \(\mu\), a ray, incident at an angle \(\theta\), on the face \(AB\) would get transmitted through the face \(AC\) of the prism provided:
| 1. | \( \theta>\sin ^{-1}\left[\mu \sin \left({A}-\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right] \) |
| 2. | \( \theta<\sin ^{-1}\left[\mu \sin \left({A}-\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right] \) |
| 3. | \( \theta>\cos ^{-1}\left[\mu \sin \left({A}+\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right] \) |
| 4. | \( \theta<\cos ^{-1}\left[\mu \sin \left({A}+\sin ^{-1}\left(\frac{1}{\mu}\right)\right)\right]\) |
1. \(60~\text{cm}\)
2. \(24~\text{cm}\)
3. \(30~\text{cm}\)
4. \(-24~\text{cm}\)
1. \(15^\circ\)
2. \(60^\circ\)
3. \(30^\circ\)
4. \(18^\circ\)
1. \({3f}\)
2. \({3\over 2}{f}\)
3. \({f}\)
4. \({2f}\)
An observer looks at a distant tree of height \(10~\text{m}\) with a telescope of magnifying power of \(20\). To the observer, the tree appears:
| 1. | \(10\) times taller |
| 2. | \(10\) times nearer |
| 3. | \(20\) times taller |
| 4. | \(20\) times nearer |
A diverging lens with the magnitude of focal length \(25~\text{cm}\) is placed at a distance of \(15~\text{cm}\) from a converging lens of magnitude of focal length \(20~\text{cm}\). A beam of parallel light falls on the diverging lens. The final image formed as:
| 1. | real and at a distance of \(40~\text{cm}\) from convergent lens |
| 2. | virtual and at a distance of \(40~\text{cm}\) from convergent lens |
| 3. | real and at a distance of \(40~\text{cm}\) from the divergent lens |
| 4. | real and at a distance of \(6~\text{cm}\) from the convergent lens |
1. \(\cos^{-1}(\sin\theta_\text{C})\)
2. \(\frac{1}{\tan^{-1}(\sin\theta_\text{C})}\)
3. \(\tan^{-1}(\sin\theta_\text{C})\)
4. \(\frac{1}{\cos^{-1}(\sin\theta_\text{C})}\)
1. \(27.5~\text{cm}\)
2. \(20.0~\text{cm}\)
3. \(25.0~\text{cm}\)
4. \(30.5~\text{cm}\)
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