A converging lens and diverging mirror are placed at a separation of 20cm. the focal length of the lens is 30cm and that of the mirror is 50 cm. where should a point Source be placed between the length and the mirror so that the light after getting reflected by the mirror and then getting transmitted by the lens comes out parallel to the principal axis?

Question

Answer

Problem Statement

A converging lens and diverging mirror are placed at a separation of 20cm. The focal length of the lens is 30cm and that of the mirror is 50cm. Where should a point source be placed between the lens and the mirror so that the light after getting reflected by the mirror and then getting transmitted by the lens comes out parallel to the principal axis?

Solution

To solve this problem, we need to use the mirror and lens formulae. We also need to understand how the light behaves when passing through a converging lens and a diverging mirror.

Understanding Light Behaviour

When light passes through a converging lens, it converges at a point called the focal point.

When light reflects off a diverging mirror, it diverges as if it is coming from a point behind the mirror.

When light passes through a converging lens and then through a diverging mirror, the light converges at the focal point of the lens, reflects off the mirror, and then diverges as if it is coming from a point behind the mirror.

If we place a point source at the position where the light converges after passing through the lens, then the light will come out parallel to the principal axis after reflecting off the mirror and passing through the lens again.

Using Mirror and Lens Formulae

We can use the mirror and lens formulae to find the position of the point source. Let the distance of the point source from the lens be x.

From the lens formula, we have:

1/f = 1/v - 1/u

where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens.

Substituting the values, we get:

1/30 = 1/(x - 20) - 1/x

Simplifying the equation, we get:

x = 60 cm

Now, we can find the position of the image formed by the lens using the lens formula:

1/30 = 1/v - 1/60

Solving for v, we get:

v = 40 cm

The distance between the mirror and the image is:

d = 20 + v = 60 cm

Using the mirror formula, we have:

1/f = 1/v + 1/u

where f is the focal length of the mirror, v is the distance of the image from the mirror, and u is the distance of the object from the mirror.

Substituting the values, we get:

1/50 = 1/(d - 60) - 1/d

Solving for d, we get:

d = 75 cm

Therefore, the distance of the object from the mirror is:

u = d - 60 = 15 cm

The position of the point source is 60 cm from the lens.

Answer

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