Question

- a) Expial
A=AXI
(b) An object of height 7cm is placed infront of a concave mirror at 27 cm whose focal
length is 18cm. Find the nature position and size of the image formed.​

Answer 1

Given :

In concave mirror,

Object height = 7 cm

Object distance = - 27 cm

Focal length = - 18 cm

To find :

The nature position and size of the image formed.

Solution :

Position of the image formed :

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

now, substituting all the given values,

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

$\dashrightarrow\sf \dfrac{1}{( - 18)} = \dfrac{1}{v} + \dfrac{1}{( - 27)}$

$\dashrightarrow\sf - \dfrac{1}{18} = \dfrac{1}{v} - \dfrac{1}{27}$

$\dashrightarrow\sf - \dfrac{1}{18} + \dfrac{1}{27} = \dfrac{1}{v}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 3 + 2}{54}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 1}{54}$

$\dashrightarrow\sf v = - 54 \: cm$

Thus, the position of the image formed is -54 cm.

Size of the image formed :

using magnification formula that is,

» 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,

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

$\dashrightarrow\sf - \dfrac{ - 54}{ - 27} = \dfrac{h'}{7}$

$\dashrightarrow\sf - 2= \dfrac{h'}{7}$

$\dashrightarrow\sf h' = - 14 \: cm$

Thus, the size of the image formed is 14cm.

Nature of the image formed :

• Image is real and inverted
• Image is enlarged