Question

Three lenses L₁, L₂ and L₃, each of focal length 40 cm, are placed coaxially. The distance between L₁ and L₂ and between L₂ and L₃ are 120 cm and 20 cm respectively. An object is kept at a distance of 80 cm to the left of lens L₁.

Find the distance of the final image formed from the object.

Answer 1

The first lens L1 has a focal length f₁ = 40 cm, and the object distance is u₁ = −80 cm (left of the lens).

Using the lens formula:

`1/v - 1/u = 1/f`

`1/v_1 - 1/-80 = 1/40`

`1/v_1 = 1/40 - 1/80`

`1/v_1 = 1/80`

v₁ = 80 cm

The first image is formed 80 cm to the right of L₁.

The distance between L₁ and L₂ is 120 cm.

The image from L₁ acts as the object for L₂.

u₂ = v₁ −120

= 80 − 120

= −40 cm

The focal length f₂ = 40 cm. Since the object is placed at the focus (u₂ = −f₂):

`1/v_2 - 1/-40 = 1/40`

`1/v_2 = 1/40 - 1/40`

`1/v_2` = 0

v₂ = ∞

The rays emerging from L₂ are parallel to the principal axis.

The distance between L₂ and L₃ is 20 cm.

Since the rays from L₂ are parallel (u₃ = ∞), they will converge at the focus of L₃.

v₃ = f₃ = 40 cm

The final image is formed 40 cm to the right of L₃.

To find the distance from the object to the final image, we sum the distances along the axis:

Object to L₁ = 80 cm

L₁ to L₂ = 120 cm

L₃ to final image = 40 cm

Total distance = 80 + 120 + 20 + 40

= 260 cm