Question

The radius of curvature of a convex mirror is 30 cm. It forms an image of an object which is half the size of the object. Find the separation between the object and the image.

Answer 1

R = 2f = 30 cm

⇒ f = 15 cm

f = 15 cm (convex mirror)

"Convex mirror ⇒ erect image ⇒ m > 0" ye line 

`m = 1/2 = (-v)/u`

⇒ `v = (-u)/2`

⇒ u = −2v

By mirror formula,

`1/v + 1/u = 1/f`

`1/v - 1/(2v) = 1/15`

⇒ `1/(2v) = 1/15`

v = 7.5 cm, u = −2v = −15 cm

Distance between image & object

= 7.5 + 15

= 22.5 cm