Question

An object is placed perpendicular to the principal axis of a convex lens of focal length $20$ . The distance of the object from the lens is $30\,cm$ . Find:
(i) the position,
(ii) the magnification and
(iii) the nature of the image formed.

Answer 1

Use the formula of the lens and substitute the known values in it to find the value of the distance of the image from the lens. Then use the formula of the magnification and substitute the value of the distance of the image and the object from the lens.

Formula used:
(1) The lens formula is given by
$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$
Where $v$ is the distance of the image from the lens, $u$ is the distance of the object from the lens and $f$ is the focal length of the object.
(2) The magnification of the lens is given by
$m = \dfrac{v}{u}$
Where $m$ is the magnification of the lens.

Complete step by step solution:
It is given that the
The focal length of the lens, $f = 20\,cm$
The distance of the object from the lens, $u = 30\,cm$
i) Using the lens formula given above,
$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$
By rearranging the given formula,
$\dfrac{1}{v} = \dfrac{1}{f} + \dfrac{1}{u}$
By cross multiplying the above equation, we get
$v = \dfrac{{fu}}{{f + u}}$
Substituting the values in the above formula,
$\Rightarrow$ $v = \dfrac{{ - 30 \times 20}}{{ - 30 + 20}}$
By simplifying the above step,
$\Rightarrow$ $v = 60\,cm$

Hence the image is at a distance of $60\,cm$ from the lens.

(ii) Let us take the magnification of the lens formula,
$m = \dfrac{v}{u}$
Substituting the values in the above step,
$m = \dfrac{{60}}{{ - 30}} = - 2$

Hence the magnification of the lens is calculated as $-2$.

(iii) The negative value of the magnification indicates that the image is so real.

Note: The magnification value determines the size of the image in comparison to that of the object. If the value of the magnification is greater than one, the formed image is larger than the object, if the magnification is less than one, then its image is smaller than the object.