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Question

A diverging lens with a magnitude of focal length 25cm is placed at a distance of 15cmfrom a converging lens of the magnitude of focal length20cm. A beam of parallel light falls on the diverging lens. The final image formed is:


A

Real and at a distance of 40cm from the convergent lens.

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B

Virtual and at a distance of 40cm from the convergent lens.

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C

Real and at a distance of6cm from the convergent lens.

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D

Real and at a distance of40cm from the divergent lens.

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Solution

The correct option is A

Real and at a distance of 40cm from the convergent lens.


Step 1. Given data,

Focal length of the diverging lens, f2=25cm

Focal length of a converging lens, f1=20cm

Distance between the two lenses, d=15cm

Step 2. Finding the distance of the image formed and its nature:

The ray diagram is shown below:

The diverging lens diverges the rays such that the rays coming from inifite appear to meet at focal point 25cmof the diverging lens.

The distance of object as appeared for the converging lens is,

u=-f2+d=-25+15=-40cm

Using the lens formula,1f1=1v-1u

Wheref1 is the focal length of the converging lens, u is the apparent distance from the converging lens, and v is the distance from the image

1v=1f1+1u

1v=120-140=140

v=40cm

The image formed is at a distance of 40cm and is real.

Hence, option A is correct.


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