Question

. An object of height 10 cm is placed in front of a convex lens having focal length of 12 cm.The object is placed at a distance of 36 cm in front of the lens. How many times is the image likely to be magnified?

Answer 1

Given: An object of height 10 cm is placed in front of a convex lens having focal length of 12 cm. The object is placed at a distance of 36 cm in front of the lens.

To find: The number of times the image is likely to be magnified.

Solution:

• To find the distance of the image from the lens, the following formula is used.

        $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

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

       $\frac{1}{v} = \frac{1}{f} + \frac{1}{u}$

          $= \frac{1}{12} + \frac{1}{36}$

          $= \frac{4}{36}$

       $v = 9 cm$

• The linear magnification produced by a spherical lens is the ratio of the size of the image formed by the lens to the size of the object, both measured perpendicular to the principal axis.  
• It is given by the formula,

        $m = \frac{v}{u}$

• Here, m is the magnification produced.

        $m = \frac{9}{36}$

            $= 0.25$

Therefore, the image is likely to be magnified by 0.25 times.