A ray of light is incident on a $\mathrm{}$\(60^\circ\) prism at the minimum deviation position. The angle of refraction at the first face (ie, incident face) of the prism is:
1. zero
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)

Two thin lenses of focal length $f_1 and f_2$ are in contact and coaxial. The power of the combination is 

1. $\sqrt{\frac{f_1}{f_2}}$                   

2. $\sqrt{\frac{f_2}{f_1}}$

3. $\frac{f_1-f_2}{f_1{f}_2}$               

4. $\frac{f_1+f_2}{f_1{f}_2}$

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 $\times {10}^9 m$ and its mean distance from the earth is $1.5\times {10}^{11} m$. What is the diameter of the sun's image on the paper?

1. $9.2\times {10}^{-4 }m$

2. $6.5 \times {10}^{-4 }m$

3. $6.5\times {10}^{-5}m$

4. $12.4\times {10}^{-4} m$

The speed of light in media ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ is $1.5\times {10}^8 \mathrm{m}/\mathrm{s}$ and $2.0\times {10}^8 \mathrm{m}/\mathrm{s}$ respectively. A ray of light enters from medium ${\mathrm{M}}_1$ to ${\mathrm{M}}_2$ at an incidence angle i. If the ray suffers total internal reflection, the value of i is

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 lens having focal length f and aperature 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. Focal length of lens and intensity of image now will be respectively

(a) f and $\frac{1}{4}$                                      (b) $\frac{3f}{4}and \frac{I}{2}$

(c) f and $\frac{3I}{4}$                                     (d) $\frac{f}{2}and \frac{I}{2}$

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 values of $\mu$ the ray can undergo total internal reflection?

1. $\mu =1.33$                             

2. $\mu =1.40$

3. $\mu =1.50$                             

4. $\mu =1.25$

Which of the following is not due to total internal reflection?

(1) Difference between apparent and real depth of a pond

(2) Mirage on hot summer days

(3) Brilliance of diamond

(4) Working of optical fibre

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. lies between $\sqrt{2}$ and 1

2. lies between 2 and $\sqrt{2}$

3. is less than 1

4. is greater than 2

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

1. 10cm,10cm

2. 15cm,5cm

3. 18cm,2cm

4. 11cm,9cm