Question

A convex mirror with a radius of curvature of 3m is used as rear view in an automobile. If a bus is located at 5m from this mirror, find the position, nature and size of the imaze.

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.
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Answer 2

Hi there,

Object Distance (u) = -5m
[ Here u is always negative for both the mirrors]

Radius of Curvature (C) = 3m
Focal length = C/2 = 3/2 = 1.5m

So, by using mirror formula,
1/v + 1/u = 1/f
1/v = 1/f - 1/u
1/v = 1/1.5 - 1/(-5)
1/v = -5 - 1.5/ 7.5
1/v = -6.5 / -7.5

v = 1.15m

The next thing we should find is magnification.
For that the formula is m = -v/u
                                        = -1.15/-5
                                        = 0.23

Here the magnification is +ve , so the nature of the image is Virtual and Erect. Not only that, image is formed on the opposite side of the object.

0.23 is small. Therefore the image is Virtual, erect and diminished.

Hope you find this answer helpful....
Thank you...