Question

A local fun house incorporates a gently curved, concave, spherical mirror into its display. When a child stands 1.2 m from the mirror, her reflection is upside down and appears to float in front of the mirror. When she stands about 0.8 m from the mirror, she sees only a blur reflected in the mirror, but when she stands about 0.5 m from the mirror, her reflection is right side up and appears to be behind the mirror. The approximate focal length of the mirror is

Answer 1

Options:

a) more than 0.8 m .

b) equal to 0.8 m .

c) between 0.5 m and 0.8 m .

d) less than 0.5 m .

Answer:

b) equal to 0.8 m .

Explanation:

Note:

An upside down image = Inverted Image

An image that appears in front of the mirror = Real image

An image that appears behind the mirror = Virtual image

Let the object distance from the pole of the mirror be u

When the child stands 1.2 m from the mirror:

u = 1.2 m ( Real and Inverted image of the child is formed)

When the child stands about 0.8 m from the mirror:

u = 0.8 m (Virtual, erect and magnified image of the child is formed)

When the child stands about 0.5 m from the mirror:

u = 0.5 m ( Virtual and erect image of the child is formed)

Note: All objects positioned behind the focal length of a concave mirror are always real. Objects start becoming virtual when they are placed on the focal length or in front of it (Close to the pole of the mirror), although objects placed on the focus has its image formed at infinity.

Since the nature of the image formed changed from real to virtual when the child stands about 0.8 m from the mirror, then the focal length is approximately equal to 0.8 m