The position of the image formed by the combination of lenses is :

Solution

Physics sir · 4 steps

Go lens by lens: each image becomes the next object. The concave lens sends the rays out parallel.

1. First lens. Take light travelling left to right as positive. For the first lens, u = -30 cm and f₁ = +10 cm, so 1/v = 1/10 - 1/30 = 1/15. The image forms at v = +15 cm, to the right of the first lens.

   1/v - 1/u = 1/f

2. Second lens. The second lens is only 5 cm away, so the rays hit it before they converge. They would have met 10 cm beyond it, so this is a virtual object with u = +10 cm. With f₂ = -10 cm, 1/v = -1/10 + 1/10 = 0, so v → ∞ and the rays leave parallel to the axis.
3. Third lens. Parallel rays falling on a convex lens meet at its focus. So the final image forms at f₃ = 30 cm to the right of the third lens. The 10 cm gap does not matter because the beam is parallel.
4. So. The final image is 30 cm to the right of the third lens, which is option (b).

The idea to keep. In a multi-lens setup, shift the origin to each lens in turn. When an image falls beyond the next lens, treat it as a virtual object with positive u. When v comes out infinite, the next lens focuses the beam at f.

Answer from the NTA final answer key. Solution by PrepWiser.