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35. To form a real point size image of a very far off object at a distance of 20 cm from the lens, focal length of lens should be

(a) 20 cm

(b) 80 cm

(d) 100 cm

Solution:
Convex lenses can converge the rays coming from long distance at their focal length and forms a point sized image.

For the above mentioned condition, we can use a convex lens of focal length 20cm so that it can form image of point size at 20cm.

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Given: Object is placed at a distance of 20cm from the lens.

To Find: focal length in order to form a real point size image.

Sol: 

The focal length of a lens is defined as the distance from the lens at which the light rays from infinity converge after refraction through the lens.

Also, the lens equations states that,

where,

  •  = focal length of the lens.
  •  = distance of the object from the lens.
  •  = distance of the image formed from the lens.

    Given that object is very far away from the lens, such that,

    Using lens equation,

    .

    Also, since the image formed is real and point sized which means the lens is convex, therefore the focal length should be positive too.

    Therefore, focal length of the lens = +20 cm.                                                                                                                                                                                                 Regards,

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