Question

An object 2.0cm in size placed 20.0cm in front of a concave mirror of focal length 10.0cm. Find the distance from the mirror at which a screen should be placed in order to to obtain a sharp image. What will be the size and nature of the image formed?

Answer 1

Given :

In concave mirror,

Object height = 2 cm

Object distance = - 20 cm

Focal length = - 10 cm

To find :

The position of the image, size and nature of the image.

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,

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

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{ - 20} = \dfrac{1}{ - 10}$

$\dashrightarrow\sf \dfrac{1}{v} - \dfrac{1}{ 20} = \dfrac{1}{ - 10}$

$\dashrightarrow\sf \dfrac{1}{v} = - \dfrac{1}{10} + \dfrac{1}{ 20}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 2 + 1}{ 20}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 1}{ 20}$

$\dashrightarrow\sf v = - 20 \: cm$

Thus, the position of the image is -20 cm.

» The Magnification produced by a mirror is equal to the ratio of the image distance to the object distance with a minus sign and is also equal to the ratio of height of the image to the height of the object .i.e.,

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

where,

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

By substituting all the given values in the formula,

$\dashrightarrow\sf - \dfrac{v}{u} = \dfrac{h'}{h}$

$\dashrightarrow\sf - \dfrac{20}{ - 20} = \dfrac{h'}{2}$

$\dashrightarrow\sf 1 = \dfrac{h'}{2}$

$\dashrightarrow\sf h' = 2 \: cm$

Thus, the height of the image is 2 cm.

Nature of the image :

• The image is formed in front of the mirror, its nature will be real and inverted.