Question

You are given three lenses L₁, L₂ and L₃ each of focal length 15 cm. A object is kept at 20 cm in front of L₁, as shown. The final real image is formed at the focus ‘I’ of L₃. Find the separation between L₁, L₂ and L₃.

Answer 1

Here f₁ = f₂ = f₃ = 15 cm

Acc. to lens makers’ formula

`1/v_1-1/u_1=1/f_1`

`1/v_1 =1/15+1/-20 =(4-3)/60 =1/60`

`v_1 =60 cm`

Now image by L₃ is formed at its focus thus the object for L₃ is placed at infinity and hence the image formed by L₂ is at infinity. This shows that for L₂ the object was placed at its focus.

Thus u₂ = 15 cm

The object for L₂ is placed at 15 cm left from L₂ which is at 60 cm right from L₁ as image of L₁ is formed at 60 cm right of L₁.

So x₁ = distance between L₁ and L₂ is

Since L₂ makes image at infinity any distance between L₂ and L₃ will make the object distance for L₃ as infinity.

So distance between L₂ and L₃ is x₂ = any length