Question

find the distance of the image when an object is placed at a distance of 10 cm in front of a concave mirror whoose radius of curvature is 8 cm. find the magnification of the above problem​

Answer 1

Given :-

• Image distance = - 10 cm

(image distance is negative as distance is always measured from the pole of the mirror )

• Radius of curvature = 8 cm

To find :-

• magnification

How to solve :-

• In order , to find magnification the image and the object distance must be known to us
• As the value of image distance is not known to us .we need to find it first by using the mirror formula
• The value of the focal length is not given to us but we can easily find it using the radius of curvature

Solution :-

We know that ,

$\implies\mathtt{f = \dfrac{R}{2}}$

here ,

• f = focal length
• R = radius of curvature

Now let's substitute the value of R in the above equation ,

$\implies\mathtt{f = \dfrac{8}{2}}$

$\implies\mathtt{f = 4 \: cm}$

We know that ,the focal length of the convex mirror is always negative

hence ,

$\implies\mathtt{f = - 4 \: cm}$

Now that we have the value of f let's find the image distance (v) by using the mirror formula

$\bigstar\boxed{\mathtt{\pink{\dfrac{1}{f}=\dfrac{1}{v}+ \dfrac{1}{u} }}}$

here ,

• f = focal length
• v = image distance
• u = object distance

Now let's substitute the given values in the above equation ,

$\implies\mathtt{\dfrac{1}{ - 4}=\dfrac{1}{v}+ \dfrac{1}{ - 20} }$

$\implies\mathtt{\dfrac{ - 1}{ 4}=\dfrac{1}{v} - \dfrac{1}{ 20} }$

$\implies\mathtt{\dfrac{1}{v} = \dfrac{ - 1}{ 4} + \dfrac{1}{ 20}}$

$\implies\mathtt{\dfrac{1}{v} = \dfrac{ - 5 + 1}{ 20} }$

$\implies\mathtt{\dfrac{1}{v} = \dfrac{ - 4}{ 20} }$

$\implies\mathtt{v = - 5 cm }$

The image is formed at a distance of 5 cm from the pole of the mirror and the negative sign denotes that the image is formed on the same side as that of the object

Magnification is given by the formula ,

$\bigstar\boxed{\mathtt{\pink{m = - \dfrac{ v}{u}}}}$

here ,

• m = magnification
• v = image distance
• u = object distance

$\implies\mathtt{m = -( \dfrac{-5}{-20})}$

$\implies\mathtt{m = -\dfrac{1}{4}}$

The magnification of the object is 1/4 and the negative sign denotes that the object is inverted .