Problem 23.11 Light reflection

[mtbgymnast]

Homework Statement

It is 171 cm from your eyes to your toes. You're standing 210 cm in front of a tall mirror.

How far is it from your eyes to the image of your toes?

Homework Equations

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The Attempt at a Solution

The answer which I got from the back of the book is 433cm.

I have the answer. Whoopie. But I have no idea how to do get the answer on my own. I know that light will hit the mirror and bounce off at an angle.
The angle of incidence is the angle between the incoming light and the normal.
The angle of reflection is the angle between the reflected ray of light and the normal.
If some one could please explain to me how to go about this problem I would greatly appreciate it.
Thanks

 

[kamerling]

your toes are 210 cm in front of the mirror. The image of your toes is 210 cm behind the mirror. (draw a picture)

 

[Moetasim]

I understand that light reflection is a fundamental principle in physics and can be explained using the laws of reflection. The law of reflection states that the angle of incidence is equal to the angle of reflection. In this problem, we can use this law to determine the distance from your eyes to the image of your toes in the mirror.

First, we need to draw a diagram to visualize the situation. From the given information, we can draw a straight line representing your height of 171 cm, and a dotted line representing the distance from the mirror to your feet, which is 210 cm. The image of your toes will be located at the same height as your actual toes, but behind the mirror. This is because the light rays from your toes will hit the mirror and bounce off at the same angle, creating the illusion of an image behind the mirror.

Now, we can use the law of reflection to determine the angle of incidence and reflection. Since the angle of incidence is equal to the angle of reflection, we can use the fact that the angle of incidence is the angle between the incoming light and the normal, and the angle of reflection is the angle between the reflected light and the normal. In this case, the normal is the imaginary line perpendicular to the surface of the mirror.

Using basic geometry, we can determine that the angle of incidence is equal to the angle between your eyes and the image of your toes in the mirror. This angle can be found by drawing a line from your eyes to the image of your toes and measuring the angle between this line and the normal. This angle will be the same as the angle of reflection, which we can use to find the distance from your eyes to the image of your toes.

To find this distance, we can use the formula tan θ = opposite/adjacent, where θ is the angle of reflection and opposite is the distance from your eyes to the image of your toes, and adjacent is the distance from the mirror to your feet. Solving for opposite, we get opposite = adjacent * tan θ. Plugging in the values of 210 cm for adjacent and the angle of reflection we found earlier, we get opposite = 210 cm * tan θ. Using a scientific calculator, we can find that tan θ = 0.4, which gives us opposite = 210 cm * 0.4 = 84 cm.

Therefore, the distance from your eyes to the image of your toes