Question

A coin 15.0 mm in diameter is placed 15.0 cm from a spherical mirror. The coin's image is 5.0 mm in diameter and is erect. Is the mirror concave or convex? What is its radius of curvature?

Answer 1

15 cm

Step-by-step explanation:

`h_(o)` = Diameter of the coin = 15 mm

`h_(i)` = Diameter of the image of coin = 5 mm

`d_(o)` = distance of the coin from mirror = 15 cm

`d_(i)` = distance of the image of coin from mirror = ?

Using the equation

`(d_(i))/(d_(o)) = (- h_(i))/(h_(o))`

`(d_(i))/(15) = (- (5))/(15)`

`d_(i)` = - 5 cm

`R` = radius of curvature

Using the mirror equation

`(1)/(d_(o)) + (1)/(d_(i)) = (2)/(R)`

`(1)/(15) + (1)/(- 5) = (2)/(R)`

`R` = - 15 cm