A rod of length \(10~\text{cm}\) lies along the principal axis of a concave mirror of focal length \(10~\text{cm}\) in such a way that its end closer to the pole is \(20~\text{cm}\) away from the mirror. The length of the image is:
1. \(15~\text{cm}\)
2. \(2.5~\text{cm}\)
3. \(5~\text{cm}\)
4. \(10~\text{cm}\)
A thin prism of angle \(15^\circ\) made of glass of refractive index \(\mu_1=1.5\) is combined with another prism of the glass of refractive index \(\mu_1=1.75.\) The combination of the prism produced dispersion without deviation. The angle of the second prism should be:
1. \(5^\circ\)
2. \(7^\circ\)
3. \(10^\circ\)
4. \(12^\circ\)
A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point \(15~\text{cm}\) from the lens on the opposite side. If the lens is removed the point where the rays meet will move \(5~\text{cm}\) closer to the lens. The focal length of the lens is:
1. \(5~\text{cm}\)
2. \(-10~\text{cm}\)
3. \(20~\text{cm}\)
4. \(-30~\text{cm}\)
The speed of light in media \(M_1\) and \(M_2\) is \(1.5\times10^{8}\) m/s and \(2.0\times10^{8}\) m/s respectively. A ray of light enters from medium \(M_1\) and \(M_2\) at an incidence angle \(i.\) If the ray suffers total internal reflection, the value of \(i\) is:
1. | equal to or less than \(\text{sin}^{-1}\left (\frac{3}{5} \right )\) |
2. | equal to or greater than \(\text{sin}^{-1}\left (\frac{3}{4} \right )\) |
3. | less than \(\text{sin}^{-1}\left (\frac{2}{3} \right )\) |
4. | equal to \(\text{sin}^{-1}\left (\frac{2}{3} \right )\) |
A ray of light is incident on a \(60^\circ\) prism at the minimum deviation position. The angle of refraction at the first face (i.e. incident face) of the prism is:
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. zero
For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:
1. | \(2\) and \(\sqrt{2}\) | lies between
2. | \(1\) | is less than
3. | \(2\) | is greater than
4. | \(\sqrt{2}\) and \(1\) | lies between
1. | the scattering of light. |
2. | the polarisation of light. |
3. | the colour of the sun. |
4. | the colour of the sky. |
A convex lens and a concave lens, each having the same focal length of 25 cm, are put in contact to form a combination of lenses. The power in dioptres of the combination is:
1. 25
2. 50
3. infinite
4. zero
A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness 3 cm and a refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark in focus again?
1. 1 cm upward
2. 4.5 cm downward
3. 1 cm downward
4. 2 cm upward