30+

a book is 9.26 cm tall and placed 22.7 cm to the left of a plane mirror. what is the height of the image formed by the mirror?

4.63

18.5

2.45

9.26

a book is 9.26 cm tall and placed 22.7 cm to the left of a plane mirror. what is the magnitude of the image distance?

22.7

9.26

24.5

11.4

you move away from a plane mirror at a speed of 1.60 m/s. at what speed does your image move away from you?

1.60 m/s

3.20m/s

6.40m/s

0.40m/s

1) 9.26 cm

Explanation:

The focal length of a plane mirror is virtually infinite. Considering the lens equation,

where f is the focal length, p is the object distance, q the image distance. If we replace f with infinity, we get

The magnification equation states that

where y is the size of the object and y' the size of the image. Substituting q=-p, we get

this means that the image produced by a plane mirror is always:

- Upright (y' is positive)

- The same size as the object

In this case, we have a book of height 9.26 cm (y=9.26 cm). This means that the magnitude of the size of the image (y') will be 9.26 cm as well.

2) 22.7 cm

As we said before, due to the infinite focal length of a plane mirror,

this means that the image produced by a plane mirror is always:

- Virtual (because q is negative)

- At the same distance from the mirror as the object

In this case, we have a book placed at 22.7 cm from the mirror (p=22.7 cm). This means that the magnitude of the distance of the image from the mirror (q) will be 22.7 cm as well.

3) 1.60 m/s

We said previously that the image produced by a plane mirror is always at the same distance from the mirror as the real object. This implies that whenever we move the object toward/away from the mirror, the distance p will alway remain equal to the distance q. But this also means that the object and the distance are moving toward/away from the mirror at the same speed.

Therefore, since in this case the person is moving away from the mirror at 1.60 m/s, the image will also move away at a speed of 1.60 m/s.

if the person is shown to have +90n, then ans is -10n.

if the person is shown to have -90n, then ans is +10n.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y