Question

in a convex lens an image is formed which is 3 times greater than the object , if the focal length of the lens is 25 cm then find the position of the object.

Answer 1

Answer:

answer is 18.75cm

Explanation:

Consider variables u = object distance (in cm), v= image distance (in cm)

Given,

-u + v = 100 ......eq (1)

Magnification = v /u = -3 (real and inverted image)

v = -3u ........eq (2)

Focal length 1/f = 1/v - 1/u ......eq (3)

Substitute eq (2) in eq (1), we get u = -25 cm

eq (2) v = -3 u = - 3 *- 25 = 75 cm

Substitute eq (2) in eq (3), we get f = - 3 u/4 = -3 * -25/4 = 18.75 cm.

Answer 2

Answer: The position of the object is $16.7 cm$ in front of the lens.

Explanation:

Given:  Focal length of convex lens, $f = 25 cm$

Distance of object, $u = ?$

Distance of image , $v$

As the image formed by a convex lens is 3 times greater than the object, so magnification of the lens is 3 and formula of magnification is:

$m = \frac{v}{u}$

$\frac{v}{u} = 3$

∴ $v = 3u$

Now using the lens formula:

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

Using  $f = 25 cm$,

$\frac{1}{25} = \frac{1}{3u} -\frac{1}{u}$

$\frac{1}{25} = \frac{1-3}{3u} = \frac{-2}{3u}$

$u = -16.7 cm$

The position of the object is $16.7 cm$ in front of the lens.

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