Flat Mirrors

And the Law of Reflection

Types of Reflection

• There are two main ways in which light reflects.

• Diffuse Reflection is caused by light hitting a rough surface and being reflected in many different directions.

• Specular Reflection is caused by light hitting a smooth surface and being reflected in only one direction.

Mirrors

• Mirrors are examples of Specular reflectors.

• Only objects that reflect light this way allow images to be “reflected”.

• Examples: Mirrors, calm water, shiny metal.

Describing Reflected Light

• When light hits a mirror, we use angles to predict the path of the light beam when it is reflected.

• The angle of incidence, ө1, is the angle the light makes normal to the mirror.

ө1

Normal Line

Describing Reflected Light

• When the light beam reflects, it creates a second angle, also measured from the normal.

• How do ө1 and ө2 compare?

ө1 ө2

Normal Line

Law of Reflection

• Ө1 and Ө2 are always going to be equal.

• We call this relationship the Law of Reflection

• The Law of Reflection states that for a reflected ray of light the angle of incidence (Ө1) and the angle of reflection (Ө2) are equal to each other.

Taking another look

ө1 ө2

Angle of incidence

Angle of reflection

So, if ө1 = 30°, ө2 = 30°

And if ө1 = 80.2°, then ө2 = 80.2°

And so on and so on…

Normal Line

Ray Diagrams Practice Problems

• When constructing a ray diagram, all diagrams must have:

• A mirror

• Normal Line

• Light Ray

• Angle of incidence

• Angle of reflection

Ray Diagrams Example 1

• When looking in a mirror, you can see the reflection of your feet. Draw a ray diagram of a light beam from your shoes to your eye.

Mirror

Ray Diagrams Example 1

ӨӨ

Angle of incidence

Angle of reflection

Mirror

Normal Line

Ray Diagram Example 2

• Mirrors are sometimes used in parking lots as a safety feature. Draw a ray diagram showing how the mirror lets you see around corners. Include a ray of incidence of 45˚.

Ray Diagram Example 2

45˚

45˚

Normal Line

Angle of Incidence

Angle of Reflection

Ray Diagram Example 3

• Construct a ray diagram showing a ray of light bouncing off the rear view mirror of your car, enabling you to see someone sitting on the passenger side front seat.

Ray Diagram Example 3

Normal

Ө Ө

Angle of Angle of

Reflection Incidence

How do we use the Law of Reflection??

• The Law of Reflection can be used to find out many different things.

ө ө

Note: Since Ө1 = Ө2, lets

just call them both Ө to keep

it simple.

Using the Law in ray diagrams

• A man stands 2 m tall at eye level looking at his shoes in a full length mirror. Construct a ray diagram of the light traveling from his shoes to his eyes.

ө

ө

Now, if we know the angle of incidence, we can calculate how far away he is from the mirror using Trigonometry.

2 m

The angle of incidence = 60°

ө= 60°2 m

1 m

1 mx

• To solve for the distance x we use the definition of tanӨ.

• tanӨ = Opposite/ Adjacent• tan(60°)= 1m / x • x= 1m / tan(60˚) So x = .578m.

Reminder:

SinӨ = Opp / Hyp

CosӨ = Adj / Hyp

TanӨ = Opp / Adj

Let’s practice a few more…