Question

The image of a distant tree is virtual and very small when viewed in a curved mirror. The image appears to be 22.9 cm behind the mirror. What kind of mirror is it?
What is its radius of curvature? (in cm)

Answer 1

Answer:

45.8 cm

Explanation:

distance of object from the mirror is infinity

distance of image, v = 22.9 cm

The mirror is convex because it is used to see the distant objects and the image formed by the mirror is erect and small.

use mirror formula

Let f be the focal length of the mirror

1 / f = 1 / v + 1 / u

1 / f = 1 / 22.9  + 1 / ∞

f = 22.9 cm

radius of curvature = 2 x focal length

radius of curvature = 2 x 22.9 = 45.8 cm

Answer 2

Answer:

A. The mirror is a convex mirror

B.  The radius of curvature of the convex mirror is -45.8 cm

Explanation:

A. Obtaining the focal length

The radius of curvature is twice the size of the focal length, the focal length is related to object and image distance with the expression below;

1 / f = 1 / v + 1 / u ...................1

f is the focal length

Since the image (v) is formed at the back of the mirror v = -22.9 cm

u is the distance of the object from the mirror  =  ∞

Substituting into equation 1

1 / f = 1 / [(-22.9)  + 1 / ∞]

1/f = 1/(-22.9)

f = -22.9

Since the focal length is negative, the mirror is  convex.

B The radius of curvature

The radius of curvature is twice the focal length of the mirror and expressed  thus;

radius of curvature = 2 x focal length

r = 2 x f

r = 2 x (-22.9 cm)

 = -45.8 cm

Therefore the radius of curvature of the convex mirror is -45.8 cm