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 

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

A 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. \(2f_1 +f_2\)
3. \(-2f_1 +f_2\)