Question

A convex mirror used for rear view on an automobile has a radius of curvature of 3m

Answer 1

1. Question⇒   A convex mirror used for rear view on an automobile has a radius of curvature of 3.00 m if the bus is located at 5.00m from this mirror .find the position,nature and size of image?

Explanation:

• given :
• R=3m
• f=R/2=3/2=1.5m
• u=5m
• v=?
• Mirror formula:
• 1/f=1/u+1/v
• by sign conventions:
• 1/1.5=1/-5+1/v
• 1/v=1/1.5+1/5⇒6.5/7.5
• v=7.5/6.5
• =1.15m
• ∴The image is virtual seen at the back of mirror.
• m=hi/ho=-v/u
• -1.15/-5=0.23
• ∴Image is erect and diminished in size by a factor of 0.23

Answer 2

Answer:

Radius of C= 3m

u = 5m

v=?

h'=?

f=R/2=3/2=1.50m( as the principal focus of convex mirror is behind the mirror)

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \\ or \: \frac{1}{v } = \frac{1}{f} - \frac{1}{u} = \frac{1}{1.50} - \frac{1}{ - 5.00} \\ = \frac{1}{1.50} + \frac{1}{5.00} = \frac{5 + 1.5}{7.5}$

$v = \frac{7.5}{6.5} = 1.15m$

The image is 1.15 m at the back of the mirror

$m = \frac{h'}{h} = - \frac{v}{u} = - \frac{1.15}{ - 5} = 0.23$

The image is virtual, erect and smaller in size by factor of 0.23