Question

an object placed at 8 cm from convex lens of f 24 cm where is the image formed and what is the magnification ​

Answer 1

Given :

In convex mirror,

Object distance : 8 cm

Focal length : 24 cm

To find :

The image distance and the magnification.

Solution :

Using mirror formula that is,

» A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula .i.e.,

$\boxed{\bf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}}$

where,

v denotes Image distance

u denotes object distance

f denotes focal length

By substituting all the given values in the formula,

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{ - 8} = \dfrac{1}{24}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{24} - \dfrac{1}{ - 8}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1 - ( - 3)}{24}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{4}{24}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{6}$

$\dashrightarrow\sf v = 6$

Thus, the position of the image is 6 cm.

We know that,

» The linear magnification produced by a mirror is equal to the ratio of the image distance to the object distance with a minus sign and it is equal to the ratio of image height and object height. that is,

$\boxed{\bf m = \dfrac{h'}{h} = - \dfrac{v}{u}}$

where,

• h' denotes height of image
• h denotes object height
• v denotes image distance
• u denotes object distance

By substituting all the given values in the formula,

$\dashrightarrow\sf m = - \dfrac{v}{u}$

$\dashrightarrow\sf m = - \dfrac{6}{ - 8}$

$\dashrightarrow\sf m = 0.75$

Thus, the magnification of the image is 0.75.