A ray of light falls on a transparent sphere as shown in the figure. If the final ray emerges from the sphere parallel to the horizontal diameter, then calculate the refractive index of the sphere. Consider that the sphere is kept in the air.
                                   
1.  $\sqrt{2}$ $$ 

2.  $\sqrt{3}$ $$

3.  $\sqrt{3/2}$ $$

4.  $\sqrt{4/3}$

A ray of light falls on the surface of a spherical glass paperweight making an angle $\alpha$ with the normal and is refracted in the medium at an angle $\beta$ . The angle of deviation of the emergent ray from the direction of the incident ray

(a) $\left(\alpha -\beta \right)$                     (b) $2\left(\alpha -\beta \right)$

(c) $\left(\alpha -\beta \right)/2$                 (d) $\left(\beta -\alpha \right)$

The slab of a refractive index material equal to 2 shown in the figure has a curved surface APB of a radius of curvature of 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in the figure. An object O is placed at a distance of 15 cm from pole P as shown. The distance of the final image of O from P as viewed from the left is:
          

An air bubble in a sphere having 4 cm diameter that appears 1 cm from the surface nearest to the eye when looked along diameter. If${}_a\mu _g$ = 1.5, the distance of bubble from the refracting surface is

1.  1.2 cm                   

2.  3.2 cm

3.  2.8 cm           

4.  1.6 cm

A convex lens made of 5 different transparent materials is used to make an image of an object placed in front of it. The number of images formed will be :

(1) 2 

(2) 3

(3) 4

(4) 5

A small air bubble is at the centre of a glass sphere of radii 5 cm. When it is viewed from outside what will be the position of the image?

Refractive index of glass is 1.5

(1) At the same place as that of object

(2) $\frac{10}{3}$ cm from the surface near the eye

(3) 7.5 cm from the surface of the sphere near the eye

(4) At infinity

Two positions of the convex lens for which the image of the object is formed on the same screen are 40 cm and 80 cm from the object. The focal length of the lens is

1.  $\frac{80}{3}cm$

2.  $\frac{40}{3}cm$

3.  40 cm

4.  80 cm

A small air bubble is present exactly at the centre of a glass sphere. Size of the image as seen from outside is of

(1) Same size

(2) Bigger

(3) Smaller

(4) May be smaller or bigger depending on the distance of observer

The following diagram shows a glass sphere of radius 10 cm with a paraxial incident ray. The refractive index of the material of the glass is

1.  2

2.  1.5

3.  1.75

4.  1.3

A spherical fishbowl of radius 15 cm is filled with water of refractive index $\frac{4}{3}$. A cat standing outside in the air at a distance of 30 cm from the centre of the fishbowl is looking at the fish. At what distance from the centre would the cat appear to the fish situated at the centre?