Q1 A thin bi convex lens of refractive index 1.5 and radius of curvature 50 cm is placed on a reflecting convex surface of radius of 100cm. A point object is placed on the principal axis of the system such that its final image coincides with itself. Find the position of object.

What I did: I first found the power of the first combination. It should be -(2*power of convex lens + 2*power of air lens between mirror and glass + power of mirror).

I can find the focal length of the glass lens and air lens using lens makers formula.

the air convex lens should be 1/f = (2/3 -1 )*(-1/50 - 1/100) ??

so using that I know the focal length of system it should be minus of previous as it becomes a mirror. The final answer 100cm... I'm geting 50cm

Q2 A parallel beam of light travelling under water with refractive index = 4/3 is refracted by a speherical air bubble. the rays are paraxial.

Find the position of final image.

I used refraction at curved surface and found the initial image position correctly. I found the final image position as -5mm from second surface. but the answer is -5/3 mm

Q3 Two thin convex lenses of focal lengths f1 and f2 are separated by a horizontal distance d ( d<f1 , d< f2) and their centres displaced by a vertical separation of D. Taking the optical centre of the lens with focal length f1 ( which is bigger in size than the second lens) is the origin. WHat would be the x,y coordinates of the focal point of lens system for a parallel beam of light incident at first lens (the f1 one) .

Any help will be appreciated... thanks. tell the question number with the hint/solution