Alocal 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

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 .

c) True. between 0.5 m and 0.8 m .

Explanation:

Optics problems with mirrors should be used the equation of the constructor and magnification

       1 / f = 1 / p + 1 / q

       M = h ’/ h = - q / p

Where f is the focal length, p the distance to the object and the distance to the image

In this equation we have two regime

For p> f the image is real, inverted,

For p> f the image is virtual and right

Let's apply these equations

Case 1

The distance to the object p = 1.2 m

.h ’is inverted and q is positive

In this case the builder's equation when the image is in front of the mirror the distance to the object is greater than the focal and inverted, so the focal length is less than 1.2 m

Case 2

The distance to the object p = 0.8 m

Case 3

Object p = 0.5 m

.h ’right

. behind the mirror

Let us examine in this case the object must have a distance less than the focal length and the image is right, therefore, the focal length is greater than 0.5 m

Case 2

The distance to the object p = 0.8 m

Let us examine case 2, in this case the distance to the object must be close to the focal point so that the image is formed near infinity, which focal length is about 0.8 m

If we collect the results of these analyzes the focal greater than 0.5 m and less than 0.8 m

The correct answer is c)

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