# Light - reflection in two facing mirrors

• HalcyonicBlues
In summary, The problem involves a plane mirror and a convex mirror placed facing each other with a 50 cm distance between them. A candle is placed on the principal axis 20 cm from the plane mirror. The task is to calculate the focal length of the convex mirror given that the distance between the two images in the plane mirror is 40 cm. The relevant equations are M = Hi/Ho = v/u and 1/f = 1/v + 1/u. The user is struggling with understanding the concept of "the distance between the two images" and whether the image in the convex mirror acts as a second object in the plane mirror. Another user suggests using ray tracing to better understand the situation.
HalcyonicBlues
Hi, thanks for stopping by.I'm studying for an exam tomorrow, I would really appreciate even just a push in the right direction!

## Homework Statement

A plane mirror and a convex mirror are placed facing each other and 50 cm apart. A candle is placed on the principal axis 20 cm from the plane mirror, as shown in Figure 17.31. If the distance between the two images in the plane mirror is 40 cm, calculate the focal length of the convex mirror.

￼￼￼￼￼￼￼

M = Hi/Ho = v/u
1/f = 1/v + 1/u

## The Attempt at a Solution

I know I should have attempted a solution, but I read it over and over and I really don't know where to start! Firstly, what does it mean by "the distance between the two images"? Does the image in the convex mirror act as a second object to the plain mirror? I don't know what I'm saying...

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HalcyonicBlues said:
Firstly, what does it mean by "the distance between the two images"? Does the image in the convex mirror act as a second object to the plain mirror? I don't know what I'm saying...

Yes, the image in the convex mirror can be considered as a second object in the plane mirror. Try ray tracing to see what is going on.

ehild

1 person

## 1. How does reflection in two facing mirrors work?

Reflection in two facing mirrors works by light bouncing off the first mirror and then bouncing off the second mirror at the same angle, resulting in an infinite number of reflections. This creates an optical illusion of depth and multiple copies of the same image.

## 2. Why do objects appear upside down when reflected in two facing mirrors?

Objects appear upside down when reflected in two facing mirrors because the light rays from the top of the object are reflected downward and the light rays from the bottom of the object are reflected upward, creating an inverted image.

## 3. Can light be reflected infinitely between two facing mirrors?

Technically, yes, light can be reflected infinitely between two facing mirrors as long as the mirrors are perfectly parallel and there is no absorption or scattering of light. However, in real life, some light will be absorbed or scattered, resulting in a decrease in the intensity of the reflections.

## 4. How does the distance between the two mirrors affect the number of reflections?

The distance between the two mirrors affects the number of reflections by determining the number of times the light can bounce back and forth between the mirrors before becoming too weak to be reflected. The closer the mirrors are, the more reflections can occur.

## 5. Why do reflections in two facing mirrors become dimmer as the distance between them increases?

Reflections in two facing mirrors become dimmer as the distance between them increases because light is not perfectly reflected, and some will be absorbed or scattered with each reflection. As the distance increases, the light has to travel a longer distance, resulting in more absorption and scattering, making the reflections appear dimmer.

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