Question

A convex mirror with a radius of curvature of 3m is used as rear view mirror for a vehicle. if a is located at 5m from mirror find the position

Answer 1

Radius of curvature of the convex mirror R = 3 m
Focal length of the convex mirror f = R/2 = 1.5 m  (positive for convex mirror)

Object (bus) distance u = − 5 m
Image distance v = ?
Mirror formula is: 1/f = 1/v + 1/u
                              1/1.5 = 1/v + 1/(−5)
1/v = 1/1.5 + 1/5
      = (5 + 1.5)/(5 x 1.5) = 6.5/7.5
v = 7.5/6.5
   = 1.15 m

Position of the image is at 1.15 m behind the mirror.

Answer 2

Given,

Radius of curvature of convex mirror is =3m.

Object distance (u) = -5m(object distance will be negative according to sign convention)

Then find the position,size and nature of image.

We know that,

Focal length is half of radius of curvature.

F = R/2

F = 3/2

F = 1.5m

The mirror formula: 1/f = 1/u+1/v

Where,

f = focal length

u = object distance

v = image distance

Now,substitute the know values in the formula.

==> 1/1.5 = 1/-5+1/v

==> 1/v = 1/1.5+1/5

==> 1/v = 5+1.5/7.5

==> 1/v = 6.5/7.5

==> v = 7.5/6.5

==> v = 1.15m

Therefore the image distance is 1.15m.

Magnification: hi/ho = -v/u

= -1.15/-5

=0.23

Therefore image is virtual seen at the back in the mirror.