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. \(\theta = 24\frac{1}{2}^{\circ}\)$$

A glass sphere $\left(\mu =\frac{3}{2}\right)$ of radius 12 cm has a small mark at a distance of 3 cm from its centre. Where will this mark appear when it is viewed from the side nearest to the mark along the line joining the centre and the mark?

A ray of light falls on a prism ABC (AB=BC) and travels as shown in figure. The refractive index of the prism material should be greater than:

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 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?

Match the corresponding entries of Column-1 with Column-2. (Where \(m\) is the magnification produced by the mirror)

An astronomical telescope has an objective and eyepiece of focal lengths \(40\) cm and \(4\) cm respectively. To view an object \(200\) cm away from the objective, the lenses must be separated by a distance:

The focal length of a glass $\left(\mu =1.5\right)$ lens in air is 20 cm. If it is dipped in water $\left(\mu =\frac{4}{3}\right)$, its focal length in water will be:

When a concave mirror of focal length f is immersed in water, its focal length becomes f', then:

Two convex lenses of focal length X and Y are placed parallel to each other. An object at infinity from the first lens forms its image at infinity from the second lens. The separation between the two lenses should be: