Final image through combination of lens and mirror

Question

An illuminated object is placed at right angle to the axis of a converging lens of focal length 15cm and 22.5cm away from it. On the other side of the lens coaxial to it a diverging lens of focal length 30 cm is placed. Find the position of final image when the lenses are 15cm apart and a lane mirror is placed perpendicular to the axis 30 cm beyond the diverging lens. (Answer: image coincides with the object)

Answer 1

Hello Pragyan,

How I wish that I could draw a diagram!

If one follows the convention that 'REAL is +' and Virtual is '-'. This is easy.

For the convex lens u = 22.5 cm, f = 15 cm and this gives us v = 45 cm. Thus there is a real Image - which means converging rays.

Converging rays Indicate Virtual Object for the concave (diverging) lens at 45-15 = 30 cm.

For this lens u = -30 cm (virtual object) , f = -30 (focus is virtual) and thus v = ∞.

 

Or Diverging rays from the real object pass thru the first lens to converge at a point 30 cm on the other side of the diverging lens.

However due to the action of the 2nd lens these rays are rendered parallel and come right back (re-trace their path) after reflection from the plane mirror and so we get an image right at the point where the object is in the first place.

 

Note the distance of the plane mirror from the diverging lens is not material to the solution.

Hope this helps.

Let me know if you need further help.

Pradip