Question

An object 2.7 cmtall is placed12 cmin front of a mirror. •What type of mirror and what radius of curvature are needed to createan upright image that is 5.4 cm in height? •What is the magnification of the image?

Answer 1

Answer:

a. Concave mirror, radius of curvature = 16 cm b. magnification = 2

Explanation:

a. Since the image is upright and larger than the object, we need a concave mirror.

We know image height, h'/object height, h = -image distance, d'/object distance, d

h'/h = -d'/d

Using the real is positive convention,

h'= + 5.4 cm, h = + 2.7 cm and d = + 12 cm.

So, + 5.4 cm/+ 2.7 cm = -d'/+ 12 cm

2 = -d'/12

d' = -2 × 12 cm

= -24 cm

Using the mirror formula 1/d + 1/d' = 2/r where r = radius of curvature of the mirror

1/+12 + 1/- 24 = 2/r

1/12(1 - 1/2) = 2/r

1/12(1/2) = 2/r

1/24 = 2/r

r/2 = 24

r = 2 × 24

r = 48 cm

b.

magnification = image height, h'/object height,h = + 5.4 cm/+ 2.7 cm = 2