Question:

The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is $40\, cm$. The area of the image is $9$ times that of the square. The focal length of the lens is :

Updated On: Apr 28, 2025
  • $36\,cm$
  • $27\,cm$
  • $60\,cm$
  • $30\,cm$
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The Correct Option is D

Solution and Explanation

If side of object square $=\ell$ and side of image square $=\ell'$ From question, $\frac{\ell'^{2}}{\ell}=9$ or $\frac{\ell'}{\ell }=3$ i.e., magnification $m = 3$ $u=- 40 \,cm$ $v= 3 \times 40= 120\, cm$ $f=?$ From formula $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ $\frac{1}{120}-\frac{1}{-40}=\frac{1}{f}$ or, $\frac{1}{f}=\frac{1}{120}+\frac{1}{40}=\frac{1+3}{120} \therefore f =30\,cm$
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Concepts Used:

Spherical Lenses

Lenses that are made by combining two spherical transparent surfaces are called spherical lenses.  In general, there are two kinds of spherical lenses. Lenses that are made by joining two spherical surfaces that bulge outward are convex lenses, whereas lenses that are made by joining two spherical surfaces that curve inward are concave lenses.

Properties of Convex lens:

  1. In this, the lenses are thicker in the middle and thinner at the edges.
  2. They have a positive focal length.
  3. It intersects the incident rays towards the principal axis
  4. These lenses are used in the camera, focus sunlight, projector microscope, simple telescope, overhead projector, magnifying glasses, etc.

Properties of Concave lens:

  1. These lenses are thinner in the middle and thicker at the edges.
  2. They have a negative focal length.
  3. It parts the incident rays away from the principal axis.
  4. These are used in the glasses, spy holes, some telescopes in the doors, etc.