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 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?

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