A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses L₁ and L₂ with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens L₁ as shown in the figure. The distance between the object and the image formed by the system of two lenses is __________ cm.

Solution

Physics sir · 4 steps

Let the first lens make an image, then treat that image as the object for the second lens.

1. First lens. Take light travelling left to right as positive. For L₁, u = -6 cm and f = +24 cm. The object is inside the focal length, so expect a virtual image on the same side as the object.

   1/v₁ = 1/f₁ + 1/u₁ = 1/24 - 1/6 = -3/24 ⇒ v₁ = -8 cm

2. Second lens. This image is 8 cm to the left of L₁, so it is 8 + 10 = 18 cm to the left of L₂. For L₂, u = -18 cm and f = +9 cm, so 1/v₂ = 1/9 - 1/18 = 1/18, giving v₂ = +18 cm.
3. Add the distances. The final image is 18 cm to the right of L₂. The object is 6 cm to the left of L₁, and the lenses are 10 cm apart.
4. So. Object to final image is 6 + 10 + 18 = 34 cm.

The common slip: 18. Stopping at the image distance from L₂ gives 18, not 34. The question asks for the distance from the object, so add the 6 cm and 10 cm as well.

The idea to keep. For lens combinations, go one lens at a time. The image of the first lens becomes the object of the next, and you measure its distance from the new lens before using the lens formula again.

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