Mammoth Memory

Normal line and two flat mirrors at right angles

When two plane mirrors are at right angles to each other a ray of light reflects from one mirror into the other and back out again.

The outgoing reflected ray is always parallel to the incident ray

Using the law of reflection and geometry we can show that the outgoing reflected ray is always parallel to the incident ray.

Ray diagram of two mirrors at right angles to each other

We can prove this as follows:

First of all put the normals in where the ray touches the mirrors and extend them so they meet each other.

Ray diagram with normal lines drawn in.

Now add the following angles.

Ray diagram with angles added.

We can see that A and B equal `90^@-(m\i\n\u\s)theta`.

No matter what angle `theta` is the incident ray and reflected ray will be parallel.

 

Let's show you with two different angles.

Example 1

Ray diagram showing angle A equals angle B

Angle A equals angle B and equal `90^@-(m\i\n\u\s)theta`

 

Example 2

Ray diagram showing angle A equals angle B again

Angle A equals angle B and equal `90^@-(m\i\n\u\s)theta`

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