When a ray of light falls on a given plate at an angle of incidence \(60^{\circ}\), the reflected and refracted rays are found to be normal to each other. The refractive index of the material of the plate is:

A medium shows relation between i and r as shown. If the speed of light in the medium is nc then the value of n is:

1. 1.5

2. 2

3. 2^–1

4. 3^–1/2

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

An air bubble in a glass slab with refractive index 1.5 (near-normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness (in cm) of the slab is:

A plane mirror is placed at the bottom of a fish tank filled with water of refractive index $\frac{4}{3}$. The fish is at a height 10 cm above the plane mirror. An observer O is vertically above the fish outside water. The apparent distance between the fish and its image is:
                         

1. 15 cm

2. 30 cm

3. 35 cm

4. 45 cm

Two slabs P & Q of transparent materials have a thickness in the ratio 2 : 5. If a ray of light takes the same amount of time to move from A to B and B to C, then the refractive index of Q with respect to P will be:

1. 0.4 

2. 2.5

3. 1.4

4. 1.85

A fish at a depth y inside the water is seeing a bird. The bird is at a height x above the water level. If the refractive index of water is $\mathrm{\mu }$, then the apparent distance of bird as seen by the fish is:

1.  x + $\mathrm{\mu }$y

2.  y + $\mathrm{\mu }$x

3.  x + $\frac{\mathrm{y}}{\mathrm{\mu }}$

4.  y + $\frac{\mathrm{x}}{\mathrm{\mu }}$

For a light incident from air on a slab of refractive index 2, the maximum possible angle of refraction is:

A beam of light composed of red and green rays is incident obliquely at a point on the face of a rectangular glass slab. When coming out on the opposite parallel face, the red and green rays emerge from:

A diverging beam of light from a point source S having divergence angle $\alpha$, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is:
   

1. Zero                                       

2. $\alpha$

3. ${\sin }^{-1}\left(1/n\right)$                           

4. $2{\sin }^{-1}(1/n)$