Question

FIND THE DISTANCE OF THE IMAGE FORM A CONVEX MIRROR IF THE OBJECT IS KEPT AT 25CM FROM IT. THE RADIUS OF CURVATURE IS 200CM

Answer 1

✬ Image Distance = 20 cm ✬

Explanation:

Given:

• Object is kept at a distance of 25 cm in front of convex mirror.
• Radius of curvature is 200 cm.

To Find:

• Distance of image from the mirror ?

Formula to be used:

• 1/f = 1/v + 1/u

Solution: Here we have

• u {object distance} = +25 cm

• v {image distance} = ?

As we know that

➟ Radius of curvature = 2F

➟ 200 = 2F

➟ 200/2 = F

➟ 100 = F

• f {focal length} = 100 cm

Substituting all the values on the above formula

$\implies{\rm }$ 1/100 = 1/v + 1/25

$\implies{\rm }$ 1/100 – 1/25 = 1/v

$\implies{\rm }$ 1 + 4/100 = 1/v

$\implies{\rm }$ 5/100 = 1/v

$\implies{\rm }$ 5v = 100

$\implies{\rm }$ v = 100/5

$\implies{\rm }$ v = +20 cm

Hence, distance of image from the mirror is 20 cm.

• As the v is positive therefore according to sign convention , the image is formed behind the mirror and is virtual.

Answer 2

Given :-

$~~~~~~~$

• Object is kept at a distance of 25cm in front of convex mirror.
• Radius of curvature of 200cm.

$~~~~~~~$

To find :-

$~~~~~~~$

• Distance of image from the mirror ?

$~~~~~~~$

$~~~~~~~~~~~~~$ $\dag$ Formula Used :

$~~~~~~~$

• $\large{\sf{\frac{1}{f} = \frac{1}{v} + \frac{1}{v} }}$

$~~~~~~~$

Solution :-

$~~~~~~~$

$~~~~~~~~~~~$ ★ Here we have,

• u [ object distance ] = +25cm
• v [ image distance ] = ?

$~~~~~~~$

$~~~~~~~~~~~~~~~~~$ ___________________

$~~~~~~~~~~~~~~~~~$ $\dag$ As we know that,

$~~~~~~~~~~~~~~~~$ ___________________

$~~~~~~~$

$\rightarrow$ $\large{\sf{Radius~of~curvature~=~2F}}$

$~~~~~~~$

$~~~~~$ $\rightarrow$ $\large{\sf{200~=~2F}}$

$~~~~~~~$

$~~~~~~~~~~$ $\rightarrow$ $\large{\sf{\frac{200}{2} = F}}$

$~~~~~~~$

$~~~~~~~~~~~~~~~$ $\rightarrow$ $\large{\underline{\boxed{\purple{\sf{100~=~F}}}}}$★

$~~~~~~~$

• f [ focal length ] = 100cm

$~~~~~~~$

★ Substituting all the values on the above formula :

$~~~~~~~$

$\implies$$\large{\sf{\frac{1}{100} = \frac{1}{v} + \frac{1}{25}}}$

$~~~~~~~$

$~~~$$\implies$ $\large{\sf{\frac{1}{100} - \frac{1}{25} = \frac{1}{v} }}$

$~~~~~~~$

$~~~~~~~~$$\implies$ $\large{\sf{1 + \frac{4}{100} = \frac{1}{v}}}$

$~~~~~~~$

$~~~~~~~~~~~~~$$\implies$ $\large{\sf{\frac{5}{100} = \frac{1}{v}}}$

$~~~~~~~$

$~~~~~~~~~~~~~~~~~~$$\implies$ $\large{\sf{5v = 100}}$

$~~~~~~~$

$~~~~~~~~~~~~~~~~~~~~~~~$$\implies$ $\large{\sf{v = \frac{100}{5} }}$

$~~~~~~~$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~$$\implies$ $\large{\underline{\boxed{\pink{\sf{v = + 20cm}}}}}$★

$~~~~~~~$

$\large\dag$ Hence,

$~~~~~~~$

• Distance of image from the mirror is 20cm.

$~~~~~~$

• As the v is positive therefore according to sign convention, the image is formed behind the mirror and is virtual.