Question

an object 5.0 CM in length is placed at a distance of 20 CM in front of a convex mirror of radius of curvature 30cm find the position of the image​

Answer 1

Given :

Object distance = -20 cm

Object height = 5 cm

Radius of curvature = 30 cm

To Find :

The position of the image.

Solution :

we know that the focal length of the spherical mirror is equal to half of its radius of curvature

f = R/2

f = 30/2 = 15 cm.

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,

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

$\dashrightarrow\sf \dfrac{1}{15} = \dfrac{1}{v} - \dfrac{1}{20}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{15} + \dfrac{1}{20}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{4 + 3}{60}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{7}{60}$

$\dashrightarrow\sf v = \dfrac{60}{7}$

$\dashrightarrow\sf v = 8.57 \: cm$

Thus, the position of the image is 8.57 cm