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

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 1

Considering these observations, we can conclude that the focal length (f) of the mirror must be between 0.5 m and 0.8 m. Option c) between 0.5 m and 0.8 m.

How to determine the approximate focal length of the mirror

To determine the approximate focal length of the mirror, use the mirror equation, which relates the object distance (o), the image distance (i), and the focal length (f) of a spherical mirror:

1/f = 1/o + 1/i

Given the information provided:

When the child stands 1.2 m from the mirror, her reflection is upside down and appears to float in front of the mirror.

When the child stands about 0.8 m from the mirror, she sees only a blur reflected in the mirror.

When the child stands about 0.5 m from the mirror, her reflection is right side up and appears to be behind the mirror.

From these observations, we can deduce the following:

The image formed when the child stands 1.2 m from the mirror is a virtual image located in front of the mirror. This indicates that the object distance (o) is positive and the image distance (i) is negative.

The image formed when the child stands about 0.5 m from the mirror is a virtual image located behind the mirror. This indicates that both the object distance (o) and the image distance (i) are negative.

Considering these observations, we can conclude that the focal length (f) of the mirror must be between 0.5 m and 0.8 m.

Therefore, the correct option is:

c) between 0.5 m and 0.8 m.

Answer 2

c) True. between 0.5 m and 0.8 m .

Step-by-step 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)