Question

an object is placed at a distance of 10 cm in front of a convex mirror of focal length 10 cm then the magnification of the image formed will be​

Answer 1

Given :

In convex mirror,

Object distance : 10 cm.

Focal length : 10 cm

To find :

The magnification of the image formed.

Solution :

First we have to find the image distance of the mirror,

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,

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

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{ - 10} = \dfrac{1}{10}$

$\dashrightarrow\sf \dfrac{1}{v} - \dfrac{1}{10} = \dfrac{1}{10}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{10} + \dfrac{1}{10}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1 + 1}{10}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{2}{10}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{5}$

$\dashrightarrow\sf v = 5 \: cm$

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,

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

$\dashrightarrow\sf m = - \dfrac{5}{ - 10} \:$

$\dashrightarrow\sf m = \dfrac{1}{2}$

$\dashrightarrow\sf m = 0.5$

Thus, the magnification of the image formed is 0.5.

Answer 2

1/2

Explanation:

if u≈f, then magnification will be 1/2 or 0.5