Question

A shop security mirror 5.0 m from certain items displayed in the shop produces one-tenth magnification.

1. What is the type of mirror?
2. What is the radius of curvature of the mirror?

Answer 1

a. The mirror is of convex type.

b. u = 5 cm

Magnification (m) = `1/10`

⇒ `1/10 = -v/-5`

⇒ v = `5/10`

⇒ v = `1/2` m

By using the mirror formula:

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

⇒ `1/(1/2) + 1/-5 = 1/f`

⇒ `1/f = 2 - 1/5`

⇒ `1/f = 9/5`

⇒ f = `5/9` m

Radius of curvature (R) = 2f 

R = `10/9` m