Question

A dentist’s mirror is placed 2.3 cm from a tooth. The enlarged image is located 6.2 cm behind the mirror. (a) What kind of mirror (plane, concave, or convex) is being used? (b) Determine the focal length of the mirror. (c) What is the magnification? (d) How is the image oriented relative to the object?

Answer 1

given, dentist's mirror is u = -2.3 cm from the tooth
the image is enlarged and is v = 6.2 cm behind the mirror ( +ve sign for behind the mirror, -ve sign for infornt of the mirror)

a. Now, among spherical mirrors, convex mirror never creates enlarged image, where as concave mirror generates large images behind the mirror when the object is placed
between the focus and pole of the mirror
hence the given mirro is concave mirror

b. focal length = f
now from mirror formula
1/v + 1/u = 1/f
-1/2.3 + 1/6.2 = 1/f
f = -3.65641025641 cm

c. magnification for mirror is m = -v/u
m = 2.6956521 ( + ve value indicated the image formed is virtual, value > 1 indicates the image is enlarged)

d. hence the image is erect, mirror reversed and enlarged compared to the original object