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

$$

A concave mirror of 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. ${\mathrm{ f}}_1+f_2$                                 

2.$$ f₁+f₂

3.$\mathrm{ \; 2}{f}_1+f_2$                               

4.$-2f_1+f_2$

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

1. 10cm,10cm

2. 15cm,5cm

3. 18cm,2cm

4. 11cm,9cm

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

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

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. $\mu =1.25$

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) $\frac{f}{2}and \frac{I}{2}$

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 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. \(60^\circ\)