Question

A convex mirror has its radius 30cm. Find the position of the image of an object placed at a distance of 18cm from the mirror

Answer 1

Given :

▪ Radius of curvature = 30cm

▪ Distance of object = 18cm

▪ Type of mirror = convex

To Find :

▪ Distance of image.

Concept :

→ X-coordinates of centre of curvature and focus of concave mirror are negative and those for convex mirror are positive. In case of mirrors since light rays reflects back in X-direction, therefore -ve sign of v indicates real image and +ve sign of v indicates virtual image.

→ Mirror formula :

$\bigstar\:\underline{\boxed{\bf{\blue{\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}=\dfrac{2}{R}}}}}$

Calculation :

$\dashrightarrow\sf\:\dfrac{1}{u}+\dfrac{1}{v}=\dfrac{2}{R}\\ \\ \dashrightarrow\sf\:\dfrac{1}{(-18)}+\dfrac{1}{v}=\dfrac{2}{30}\\ \\ \dashrightarrow\sf\:\dfrac{1}{v}=\dfrac{2}{30}+\dfrac{1}{18}\\ \\ \dashrightarrow\sf\:\dfrac{1}{v}=\dfrac{36+30}{540}\\ \\ \dashrightarrow\sf\:v=\dfrac{540}{66}\\ \\ \dashrightarrow\underline{\boxed{\bf{\red{v=8.18cm}}}}$

Answer 2

GIVEN:

• Type of mirror ➻ convex mirror
• Distance of object ➻ 18 cm
• Radius of curvature ➻ 30cm

TO FIND:

• Position of image

SOLUTION:

Using the mirror formula

1/v + 1/u = 1/f = 2/R

Where

• v ↦ Position
• u ↦Distance of object
• R ↦ Radius of curvature

↦ 1/-18 + 1/v = 2/30

↦ 540/66 = 1/v

→ 8.18 cm

Hence, Position of image = 8.18 cm