Question

You are given three lenses L₁, L₂ and L₃ each of focal length 20 cm. A object is kept at 40 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 = 20 cm

Now, u₁ = −40 cm

From lens makers formula

`1/V_1-1/u_1=1/f_1`

`1/V_1=1/f_1  + 1/u_1`

`= 1/20 + 1/-40`

`= (2-1)/20 =1/40`

`V_1 =40 cm`

Here, image by L₃ is formed at focus. So the object should lie at infinity for L₃. Hence, L₂ will produce image at infinity. So, we can conclude that object for L₂ should be at its focus.

But, we have seen above that image by L₁ is formed at 40 cm right of L₁ which is at 20 cm left of L₂ (focus of L₂).

So X₁ = distance between L₁ and L₂ = (40 + 20) cm

= 60 cm

Again distance between L₂ and L₃ does not matter as the image by L₂ is formed at infinity so X₂ can take any value.