Question

a convex lens of focal length is 25 cm calculate the object distance if the image is to be formed in opposite side of the lens at a distance of 75cm what is the nature of image
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Answer 1

Answer:

1. u = -37.5 cm

2. Nature of image is real, inverted and enlarged.

Explanation:

Given

Focal length f = +25 cm ( +ve as lens is convex)

Image distance v = +75 cm(+ve as image is on right side of lens)

Calculation

Lens formula for thin lens is given by

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

Using the given values of v and f, we get

$\frac{1}{75} - \frac{1}{u} = \frac{1}{25}$

$\frac{1}{75} - \frac{1}{25} = \frac{1}{u}$

$\frac{1 - 3}{75} = \frac{1}{u}$

$\frac{1}{u} = - \frac{2}{75}$

$u = - \frac{75}{2}$

$u = - 37.5 \: cm$

Hence object is 37.5 cm from the lens. As image is formed on opposite side of the convex lens, the image is real in nature.

Magnification of image is given by

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

$so \: m = \frac{75}{ - 37.5}$

$or \: m = - 2$

From this we can conclude that

1. -ve sign of m indicates that the image is inverted.

2. magnitude of m is greater than 1 which indicate that image is enlarged.

Hence, nature of image is real, inverted and enlarged.