A ray of light is incident at an angle of incidence, \(i\), on one face of a prism of angle \(A\) (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is \(\mu,\) the angle of incidence \(i\) is nearly equal to:

1.	\(\mu A \)	2.	\(\frac{\mu A}{2} \)
3.	\(A / \mu \)	4.	\(A / 2 \mu\)

A concave mirror of the focal length \(f_1\) is placed at a distance of \(d\) from a convex lens of focal length \(f_2\). A beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance \(d\) must be equal to:
1. \(f_1 +f_2\)
2. \(-f_1 +f_2\)
3. \(2f_1 +f_2\)
3. \(-2f_1 +f_2\)

The magnifying power of a telescope is \(9\). When it is adjusted for parallel rays the distance between the objective and eyepiece is \(20\) cm. The focal lengths of lenses are:

1.  Difference between apparent and real depth of the pond

2.  Mirage on hot summer days

3.  Brilliance of diamond

4.  Working of optical fiber

A ray of light traveling in a transparent medium of refractive index $\mu$ falls on a surface separating the medium from the air at an angle of incidence of 45 °. For which of the following value of $\mu$ the ray can undergo total internal reflection?

1. $\mu =1.33$

2. $\mu =1.40$

3. $\mu =1.50$

4. $\mu =1.25$

A lens having focal length f and aperture of diameter d forms an image of intensity I . Aperture of diameter $\frac{d}{2}$ in central region of lens is covered by a black paper. The focal length of lens and intensity of image now will be respectively :

1. f and $\frac{1}{4}$

2. $\frac{3f}{4} and \frac{I}{2}$

3. f and $\frac{3I}{4}$

4. $\frac{f}{2} and \frac{I}{2}$

Two thin lenses of focal lengths f₁ and f₂ are in contact and coaxial. The power of the combination is :

1.  $\sqrt{\frac{{\mathrm{f}}_1}{{\mathrm{f}}_2}}$

2.  $\sqrt{\frac{{\mathrm{f}}_2}{{\mathrm{f}}_1}}$

3.  $\frac{{\mathrm{f}}_1+{\mathrm{f}}_2}{{\mathrm{f}}_1{\mathrm{f}}_2}$

4.  None of the above

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 x10⁹ m and its mean distance from the earth is 1.5 x 10¹¹ m. What is the diameter of the sun's image on the paper?

1.  $9.2\times {10}^{-4} \mathrm{m}$

2.  $6.5\times {10}^4 \mathrm{m}$

3.  $6.5\times {10}^{-5} \mathrm{m}$

4.  $12.4\times {10}^{-4} \mathrm{m}$

A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels up-to-the surface of the liquid and moves along its surface(see figure). 
 
How fast is the light traveling in the liquid?

1. $1.8\times {10}^8 m/s$

2. $2.4\times {10}^8 m/s$

3. $3.0\times {10}^8 m/s$

4. $1.2\times {10}^8 m/s$