In the figure shown the angle made by the light ray with the normal in the medium of refractive index $\sqrt{2}$ is:
                 
1. \(30^{\circ}\)$$

2. \(60^{\circ}\)$$

3. \(90^{\circ}\)$$

4. None of these

A light ray is incident at an angle of  \(30^{\circ}\) on a transparent surface separating two media. If the angle of refraction is \(60^{\circ}\), then the critical angle is:

1. ${\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$

2. ${\sin }^{-1}\left(\sqrt{3}\right)$

3. ${\sin }^{-1}\left(\frac{2}{3}\right)$

4. \(45^{\circ}\)$$

A plane mirror approaches a stationary person with acceleration of 10 ms^–2. The acceleration of his image as seen by the person, will be:

A fish is a little away below the surface of a lake. If the critical angle is \(49^{\circ}\), then the fish could see things above the water surface within an angular range of \(\theta^{\circ}\) where:
1. \(\theta = 49^{\circ}\)$$
2. \(\theta = 90^{\circ}\)$$
3. \(\theta = 98^{\circ}\)$\mathrm{}$
4. \(\theta = 24\frac{1}{2}^{\circ}\)$$

An object is placed at a point distance \(x\) from the focus of a convex lens and its image is formed at \(I\) as shown in the figure. The distances \(x\) and \(x'\) satisfy the relation:

   
1. \(\frac{x+x'}{2} = f\)
2. \(f = xx'\)
3. \(x+x' \le 2f\)
4. \(x+x' \ge 2f\)

The diameter of the eye-ball of a normal eye is about 2.5 cm. The power of the eye lens varies from:

1. 2 D to 10 D

2. 40 D to 32 D

3. 9 D to 8 D 

4. 44 D to 40 D

In total internal reflection when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be the angle of refraction?

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?

Focal length of objective lens and eyepiece of an astronomical telescope are 200 cm and 10 cm respectively. The length of telescope for maximum magnification is nearly:

1. 207 cm

2. 210 cm

3. 204 cm

4. 220 cm

On an optical bench a point object is placed at the mark of 10 cm, a convex lens of focal length 15 cm at the mark of 40 cm and a concave lens of focal length 15 cm placed at the mark of 60 cm. The final image is formed at the mark of: (point object and two lenses are coaxial)

1. 30 cm

2. 80 cm

3. 90 cm

4. infinity