Question

A object of height 3.3 cm is placed 36.1 cm in front of a spherical mirror. Suppose it is desirable to produce a virtual image that is upright and 1.4 cm tall.

(a) Should a concave or convex mirror be used?

b) Where is the image located?

c) What is the focal length of the mirror?

d) What is the radius of curvature of the spherical mirror?

Answer 1

(a)

A concave mirror should be used.

If the image height to object height ratio is positive because the image is upright. Upright images have positive magnifications. This means the image height is negative. This means the image distance has to be positive. Convex mirrors only produce negative image distances.

(b)

The image distance is 15.32 cm.

We can use the ratio of the image height to object height set equal to the ratio of the image distance to object distance to determine the image distance. This allows us to solve for the image distance. d_i is the image distance and d_o is the object distance. h_i is the image height and h_o is the object height.

h_i  / h_o = d_i/ d_o

1.4 / 3.3 = d_i / 36.1

d_i =15.32 cm

(c)

The focal length of the mirror is 10.76 cm.

We can use the mirror equation to determine the image distance. f is the focal point, d_i is the image distance and d_o is the object distance.

1/f=1/d_i+1/d_o

1/f=1/15.32+1/36.1

f =10.76 cm

(d)

The radius of curvature is 21.52 cm.

The radius of curvature is twice the focal length or (2)(10.76) = 21.52 cm.