Question

1. A convex mirror with a radius of curvature of 3 m is used as rear view mirror for a vehicle
If a bus is located at 5 m from this mirrot, find the position, nature and size of the image 9.​

Answer 1

Given :-

• Radius of curvature of convex mirror , R = 3 m

(since, convex mirror is used as rear view mirror)

• position of object , u = - 5 m

To find :-

• position , Nature and Size of image

Formula used :-

• Relation b/w Radius of curvature (R) and focal length (f) of mirror

      f = R / 2

• Mirror formula

       1 / f = 1 / v + 1 / u

(where f is focal length of mirror , v is position of image and u is position of object)

• Formula for magnification of mirror

       m = - v / u

(where m is magnification of mirror , v is position of image , u is position of object)

Solution :-

Calculating focal length of mirror

→ f = R / 2

→ f = 3 / 2  m = 1.5 m

Calculating position of image

using mirror formula

→ 1 / f = 1 / v  +  1 / u

→ 1 / 1.5 = 1 / v  +  1 / (-5)

→ 1 / v = 1 / 1.5  +  1 / 5

→ 1 / v = 10 / 15  +  1/5

→ 1 / v = ( 10 + 3 ) / 15

→ 1 / v = 13 / 15

→ v = 15 / 13  m = 1.15 m

Calculating magnification of image

Using formula for magnification of mirror

→ m = - v / u

→ m = -(1.15) / -5

→ m = 0.23

so,

● Position of image is 1.15 m behind the mirror.

● Nature of image is virtual and erect .

● Size of image is smaller than size of object by a factor of 0.23