Question

20. A concave shaving mirror is designed so that the virtual image is twice the size of the object, when the distance between the object and the mirror is 15 cm (a) Determine the radius of curvature of the mirror . (b) Draw a ray diagram to scale showing this situation [Ans: 60 cm​

Answer 1

Answer:

Radius of curvature = - 60 cm

Explanation:

Given :

$\frac{size of image }{size of object}$  =$\frac{h_{I} }{h_{O} }$ = 2

object distance  u = -15 cm

Since image is virtual, magnification is positive

magnification m = $\frac{h_{i} }{h_{o} }$ = + 2

Also m = - v/u = 2

               -v/(-15) = 2

                 v = + 30 cm

From Mirror formula

1/f = 1/v + 1/u

    = 1/30 - 1/15

     = - 1/30

∴ f = - 30 cm

∴ Radius of curvature R = 2f = - 60 cm

Answer 2

Answer:

sizeofobjectsizeofimage 

 =\frac{h_{I} }{h_{O} }hOhI = 2

object distance  u = -15 cm

Since image is virtual, magnification is positive

magnification m = \frac{h_{i} }{h_{o} }hohi = + 2

Also m = - v/u = 2

               -v/(-15) = 2

                 v = + 30 cm

From Mirror formula

1/f = 1/v + 1/u

    = 1/30 - 1/15

     = - 1/30

∴ f = - 30 cm

∴ Radius of curvature R = 2f = - 60 cm