Question

a screen is placed 80 cm from an object. the image of the object on the screen is formed by a convex lens at two different locations separated by 10 cm. calculate the focal length of the lens used ​

Answer 1

Given:

• A screen is placed 80 cm from an object.
• The image of the object on the screen is formed by a convex lens at two different locations separated by 10 cm.

To Find:

• Calculate the focal length of the lens.

Solution:

The image of the object can be located on the screen for two-position of convex lens such that u and v are exchanged.

The separation between two positions of the lens is, d = 10 cm

From the figure,

       $u + v = 80cm$                   $................. eq (i)$

       $v -u = 10 cm$                   $................. eq (ii)$

After solving equations,

        $v =45cm,$

        $u = 35cm$

From lens formula,

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

      ⇒     $\frac{1}{f} = \frac{1}{45} + \frac{1}{35}$

​       ⇒     $\frac{1}{f} = \frac{35 + 45 }{45 \times 35}$

​       ⇒    $\frac{1}{f} = \frac{80 }{45 \times 35}$

      ⇒     $f= \frac{1575}{80}$

     ⇒     $f= 19.68 cm$

Thus, The focal length is $19.68cm$