In the following diagram, what is the distance x if the radius of curvature is R = 15 cm?

1. 30 cm

2. 20 cm

3. 15 cm 

4. 10 cm 

The following diagram shows a glass sphere of radius \(10~\mathrm{cm}\) 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

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:
          

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 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?

In a glass ($\mu$ = 1.5) sphere with a radius of 10 cm, there is an air bubble B at a distance of 5 cm from C. The distance of the bubble from the surface of the sphere (i.e., point A) as observed from point P in the air will be:

A mark on the surface of sphere (µ = 3/2) is viewed from a diametrically opposite position. It appears to be at a distance \(15~\mathrm{cm}\) from its actual position. The radius of sphere is:
1. 15 cm
2. 5 cm
3. 7.5 cm
4. 2.5 cm

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 concave mirror of the 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. $f_1+f_2$

2. $-f_1+f_2$

3. $2f_1+f_2$

4. $-2f_1+f_2$