Angle of Incidence: Definition & Formula

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  • 0:01 What is an Angle of Incidence?
  • 0:54 Absorption,…
  • 2:48 Snell's Law
  • 6:23 Lesson Summary
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Lesson Transcript
Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

Discover what an angle of incidence is and how it relates to light. Then dive further into learning the related topics of incident angles with the reflection and refraction of light.

What Is an Angle of Incidence?

If you have ever looked at a white light being shined into a prism, the main thing you probably noticed is it being turned into a rainbow. However, did you notice that the light didn't travel straight through the prism? The light changes direction when it enters the prism, and it changes again when it leaves. This bending of light isn't something that's unique to prisms. It's a common occurrence in translucent and transparent materials. We have even come up with unique names for the angles at which the light enters and travels through the material. The angle at which the light enters is called the angle of incidence. The angle of incidence can be defined as the angle between the oncoming ray of light and the normal vector of the surface of the material it is coming into contact with. The normal vector is a perpendicular vector from a plain or surface of an object.

Normal Vector and Angle of Incidence
normal vector and angle of incidence diagram

Absorption, Reflection and Refraction

There are three possibilities for what can happen to the light after it comes into contact with an object. The first is absorption. In absorption, the light ray travels no further; it is taken into the object and transformed into energy. This most often takes the form of heat. The second is reflection, where the light ray is bounced off the material instead of absorbed. The final possibility is refraction, in which the light penetrates the object, but instead of being turned into internal energy, it changes direction and continues to travel through the material as light.

Refraction of Light in a Plastic Block
image of light being refracted in a plastic block

It's important to note that light does not often do just one of those three possibilities; rather, it travels in a combination of them. For example, we see color because objects reflect the visible light spectrum of the corresponding colors we see back to our eyes, but they absorb the other wavelengths of the visible light spectrum. Another example would be translucent objects. A translucent material, as opposed to a transparent one, only lets some of the light travel through it and absorbs and reflects the rest of it.

With absorption, there are no further relations between the angle of incidence and what happens to the ray of light, but with reflection and refraction, there is more to learn.

Law of Reflection

The relation between the reflected light ray and the incident light ray is governed by the law of reflection. The law of reflection states that the angle between the reflected ray and the normal vector is equal to the angle of incidence. Mathematically this is expressed by the following simple relation:

thetaI = thetaR

thetaI = angle of incidence

thetaR = angle of reflection

So, if you know either the angle of reflection or the angle of incidence, you automatically know the other as well.

Reflection Diagram
reflection diagram

Snell's Law

Have you ever been spear fishing, or seen it done on television? The fisherman stands in or above shallow water and tries to spear the fish as they swim by. If they try to hit the fish exactly where they see it, they will miss. The fish is not where it seems to be from above the water. This is an effect of refraction. Light bending as it enters the water is what causes the fish to appear in a different spot from where it actually is.

Much like with the angle of reflection, there is also a relation between the angle of incidence and the angle of refraction. When light enters from one medium into another, it can bend to some degree. The calculation of what degree the light will bend is known as the law of refraction, or Snell's Law. The degree to which the light bends is dependent on both the incidence angle entering the second medium and the speed at which the light travels through the two mediums. The relationship between the speed of light and refraction is given in the index of refraction. You will need to understand the index of refraction in order to understand Snell's Law.

n = c / v

n = index of refraction

c = speed of light in a vacuum

v = average speed of light in a medium

While the speed of light in a vacuum is constant, the speed of light in other mediums can vary, and consequently they have different indices of refraction. Some common examples can be seen in this table.

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