Question

Example 10.1
A convex mirror used for rear-view on an automobile has a radius of
curvature of 3.00 m. If a bus is located at 5.00 m from this mirror.
find the position, nature and size of the image.​

Answer 1

Given :

• Radius of Curvature (R) = 3 m
• Object Distance (u) = - 5 m
• Convex Mirror

To Find :

• Nature, position, size of Image

Solution :

We have to find focal length of the mirror :

➠ R = 2f

⇒f = R/2

⇒f = 3/2

⇒f = 1.5

$\therefore$ Focal length of convex mirror is 1.5 m

Use mirror Formula

➠ 1/f = 1/v + 1/u

⇒1/v = 1/f - 1/u

⇒1/v = 1/1.5 - (-1/5)

⇒1/v = 1/1.5 + 1/5

⇒1/v = (10 + 3)/15

⇒1/v = 13/15

⇒v = 15/13

⇒v = 1.15 m

$\therefore$ Image is formed at distance of 1.15 m from mirror

_______________________________

➠m = -v/u

⇒m = -1.15/-5

⇒m = 1.15/5

⇒m = 0.23

• Image is Virtual and erect

Answer 2

Answer:

Given –

• Radius of curvature = 3.00 m
• Convex mirror
• Object - Bus
• Object distance = 5.00 m

To Find –

• Position of the Image
• Nature of the Image
• Size of the Image

Solution –

Formula used – Mirror Formula : 1/v + 1/u = 1/f

Radius of curvature = 3.00 m

Focal length = 1.5 m

Object Distance = -5.00 m

➸ 1/v + 1/-5 = 1/1.5

➸ 1/v = 1/1.5 + 1/5

➸ 1/v = (5 + 1.5)/7.5

➸ 1/v = 6.5/7.5

➸ v = + 1.15 m

The position of the Image : Behind the mirror, Between Pole and the Focus of the mirror.

The nature of the Image : Virtual and Erect.

The size of the Image : Diminished.

[Diagram in the attachment.]