Reflection of Light - Online Tutor, Practice Problems & Exam Prep

Light travels in straight lines as rays, a concept central to geometric optics. When light reflects off a surface, such as a mirror, the angle of incidence (θ_I) equals the angle of reflection (θ_R), described by the law of reflection: $\theta$_I=θ_R. Angles are measured relative to the normal, a line perpendicular to the surface. Understanding these principles is crucial for solving problems involving reflection, particularly in calculating angles using trigonometric functions.

Law of Reflection

Welcome back, everyone. In this video, we're going to continue talking about light. We're going to talk about light as a ray rather than a wave. We'll also talk about something that's called the law of reflection, which is a very straightforward and pretty intuitive equation. Let's get started.

So this actually sort of brings us to an area of physics, which we call geometric optics, which basically says that light travels in a straight line and travels in a straight line as a ray, as a light ray. So you'll see these types of diagrams all the time with these arrows. Those are basically just light rays, and we'll see that light's interacting with a bunch of different objects like mirrors and lenses and things like that. Light travels as a ray even though it's made up of a bunch of waves. We said that light is an electromagnetic wave, but it always just travels in a particular direction here at a fixed speed. And so we can just model light like that as an arrow, that's traveling at a fixed speed.

Alright? So let's actually talk about the first situation that we'll encounter which is called reflection. And that's what happens when you have light that hits a flat or shiny surface, something like a mirror or a polished metal. So when light rays come in and hit a mirror at an angle, so this is going to be some angle theta here, then they reflect. And you've probably seen this all the time before. If you've looked at a mirror or if you've ever shined like a laser pointer at a mirror or something, you can see there's sort of like this beam of light and it kind of just bounces off the mirror. And so it reflects. That's called reflection. And what's really interesting about this angle or this reflected ray is that it always reflects at the exact same angle that it came in. So in other words, this theta is exactly equal to this theta. They always will be.

Now these two thetas have names, by the way. The first one is called the angle of incidence. You can kind of remember this because it sounds like incoming. Incident is incoming light. So this is given as theta_I. And the second one is called the angle of reflection. Not very creative, but it's the reflected ray. And so this angle here is called theta_R. Now these two angles are exactly the same, so we can actually just write this as an equation:

θ I = θ R

This is sometimes called the law of reflection and it's pretty straightforward, pretty intuitive. Whatever it comes in as is whatever it has to leave as.

Now what's really important that you might have noticed about these diagrams is that these angles have been drawn not relative to the horizontal like we normally do in physics. They've been drawn relative to this black line here. And that's actually really important. The one thing that you have to remember about geometric optics is that your angles should always be measured relative to the normal. Now we've seen that word before, normal. Normal just means perpendicular to the surface. So the words just make a 90 degree angle. These lines will always be drawn for you. So this normal line over here, and it's basically just telling you where 90 degrees is.

Alright? So you have to make sure that your angles are measured relative to this normal. Otherwise, you're going to get the wrong answer. Alright? So be really, really careful about that. Alright. But that's really all there is to it for reflection.

So let's just go ahead and take a look at our first problem here. Alright. So we have a laser that we're going to shine in a flat mirror that's on the ground. We want the laser beam to hit this point on the wall, and this point is actually 4 meters away from where the laser point hits the mirror. So this is going to be 4 meters, and it's also 2 meters above the floor. So in other words, this is just 2 meters over here. Alright?

So we want to actually calculate what's the angle of incidence. Okay? So this angle of incidence, remember, is just the incoming angle, theta_I. Alright? So then how do we do that? How do we calculate theta_I? Well, the one thing that we've seen about theta_I is that theta_I is equal to theta_R. But they're exactly the same. So if you don't know one of them, then you obviously don't know the other one. Right? So what's tricky about these problems is not the theta_I equals theta_R. It's what you have to do to get those angles. Alright?

So take a look here because, I have no information about any of the distances involved on the left side of the diagram, but I do have some information about the distances here. I've got 4 meters and 2 meters. So if I'm trying to figure out one of these angles here, hopefully, you figured out by now that you're going to have to solve some kind of triangle. That's what's tricky about these problems. It's not really the theta_I equals theta_R. It's what you have to do to get those equations, which is usually some trig. Alright?

So we can see here that this kind of looks sets up a little triangle like this, but what's really, really important about this, you know, what you have to be really careful about here is that when you use your equations in this format for sine, cosine, and tangent, be very careful because usually you're going to be solving for this angle over here. We've already said that this angle is going to be the bad one, so you don't want to solve for that. Instead, what we can do is we can actually sort of flip this triangle, and we could sort of draw like an inverted one. And the distances are still the same. This is going to be 4, and this is going to be 2. Now what's good about this is that now when you solve for your sine, cosine, tangent, it's going to have this angle, which you want. That's the good one. Alright?

So which formula are we going to use to solve for this theta here? We don't have the hypotenuse, so all we can use is actually just the tangent. So this is going to be:

tangent   of  θ R = 4 2

If you take the inverse tangent, theta_R is equal to the inverse tangent of 4 over 2, and what you'll get is 63 degrees. Alright? So that is your angle of incidence, and it's also your angle of reflection. So this is 63 degrees, and this is also 63 degrees. Alright? So that's all there is to it. Alright?

So let's move on now because I have actually one last conceptual point. By the way, problems will always involve reflections. There's two different types of reflections. This is only a conceptual thing. You'll never have to solve any problems like this. But problems will always involve specular reflection from smooth surfaces instead of diffuse reflection from rough surfaces. So in other words, you can kind of always assume that your surfaces are going to be perfectly flat and that light rays will always perfectly bounce at the right angle. That's called specular reflection, versus diffuse reflection, which kind of, like, you know, assumes that there's, you know, rough points or whatever, and the light will just scatter off in different directions. Alright?

So that's just a conceptual point you might need to know. Anyways, that's it for this one. Let me know if you have any questions.

A light ray strikes a horizontal surface at a 60° angle. The reflected ray then strikes a wall 2.5m above the reflective surface. How far is the wall from the point where the incident light ray strikes the surface?

• A. 4.33m
• B. 1.44m
• C. 2.5m
• D. 0.69m

Here’s what students ask on this topic:

What is the law of reflection in geometric optics?

The law of reflection in geometric optics states that when a light ray reflects off a surface, the angle of incidence (θ_I) is equal to the angle of reflection (θ_R). This can be expressed mathematically as:

$\theta$_I=θ_R

Both angles are measured relative to the normal, which is a line perpendicular to the surface at the point of incidence. This principle is fundamental in geometric optics and is used to predict the behavior of light when it encounters reflective surfaces like mirrors.

How do you calculate the angle of incidence in a reflection problem?

To calculate the angle of incidence (θ_I) in a reflection problem, you need to know the distances involved and use trigonometric functions. For example, if a laser beam hits a mirror and you know the horizontal and vertical distances from the point of incidence to a target point, you can form a right triangle. Using the tangent function:

$\tan (\theta$_R)=oppositeadjacent

Then, find θ_R using the inverse tangent:

$\theta$_R=tan⁻¹(oppositeadjacent)

Since θ_I = θ_R, this will give you the angle of incidence.

What is the difference between specular and diffuse reflection?

Specular reflection occurs when light reflects off a smooth surface, such as a mirror, where the angle of incidence equals the angle of reflection. This type of reflection produces clear and defined images. Diffuse reflection, on the other hand, happens when light reflects off a rough surface, scattering in many directions. This scattering prevents the formation of clear images. In geometric optics problems, we typically assume specular reflection for simplicity and accuracy in calculations.

Why are angles in geometric optics measured relative to the normal?

In geometric optics, angles are measured relative to the normal because the normal line is perpendicular to the surface at the point of incidence. This standard reference ensures consistency and accuracy in calculations. Measuring angles relative to the normal simplifies the application of the law of reflection, which states that the angle of incidence equals the angle of reflection. Using the normal as a reference helps avoid confusion and errors in determining the correct angles for light rays interacting with surfaces.

How does the law of reflection apply to mirrors?

The law of reflection applies to mirrors by dictating that the angle at which light hits the mirror (angle of incidence) is equal to the angle at which it reflects off the mirror (angle of reflection). This principle allows us to predict the path of light rays when they encounter a mirror. For example, if a light ray strikes a mirror at a 30-degree angle relative to the normal, it will reflect off the mirror at the same 30-degree angle on the other side of the normal. This predictable behavior is crucial for designing optical devices and solving reflection problems.