A parallel beam of light is incident on diverging lens of focal length 12cm. The emergent beam passes through a converging lens of focal length 20cm placed coaxial with it. The beam which finally emerges from the converging lens,comes out parallel. What is the separation of the lenses? Illustrate your answer with a diagram.

Question

A parallel beam of light is incident on diverging lens of focal length 12cm. The emergent beam passes through a converging lens of focal length 20cm placed coaxial with it. The beam which finally emerges from the converging lens,comes out parallel. What is the separation of the lenses? Illustrate your answer with a diagram.

Answer 1

12 cm + (lens separation)= 20 cm

lens separation = 8 cm

We don't do illustrations.

The rays leaving the diverging lens expand from a point 12 cm in front of that lens. That same point is the focal point of the converging lens, 20 cm in front of it.

Answer 2

To find the separation of the lenses, we can use the lens equation and the concept of refraction at the interface between the lenses.

The lens equation relates the object distance (u), the image distance (v), and the focal length (f) of a lens:

1/f = 1/v - 1/u

Let's break down the problem step by step.

Step 1: Determine the focal length of the diverging lens.
Given that the diverging lens has a focal length of 12 cm, we can use the lens equation. In this case, since the emergent beam passes through the diverging lens and comes out parallel, the image distance (v) will be at infinity (∞).

1/f = 1/v - 1/u
1/12 = 1/∞ - 1/u

Since 1/∞ is considered negligible, the equation simplifies to:
1/12 = 0 - 1/u
1/u = -1/12
u = -12 cm

So, the object distance (u) of the diverging lens is -12 cm, indicating that the object is located 12 cm to the left of the lens.

Step 2: Determine the object distance for the converging lens.
Since the emergent beam from the diverging lens passes through the converging lens and comes out parallel again, the object distance (u') for the converging lens will be at infinity (∞).

So, the equation becomes:
1/f = 1/v' - 1/u'
1/20 = 1/∞ - 1/u'
1/u' = 1/20
u' = 20 cm

Therefore, the object distance (u') for the converging lens is 20 cm.

Step 3: Determine the separation of the lenses.
The separation of the lenses is the distance between their respective optical centers. We can find this distance by subtracting the object distance of the converging lens from the object distance of the diverging lens (since they are placed coaxially).

Separation = | u - u' |
= | -12 - 20 |
= 32 cm

So, the separation between the lenses is 32 cm.

Here is a diagram to illustrate the setup:

Diverging Lens
|
L1 | L2 Parallel beam
|
| separation = 32 cm
|
------------
Converging
Lens