PhET Bending Light Simulation
See how light refracts when it passes through different types of materials (glass, water, etc).
PhET Geometric Optics Simulation
See how different lenses (and their properties) create images of objects.
Hello there! Welcome to lecture 28: reflection and refraction!
Every time you look in a mirror, take a photo, use eyeglasses, or look through a window, you’re experiencing reflection and refraction. Understanding how light travels enables us to grasp how the simple concepts of reflection and refraction affect our lives.
Each of the following concepts will be discussed in this video: the principle of least time, reflection, mirrors, refraction, and lenses.
The principle of least time
Light travels from one point to another using the principle of least time. That is to say, light does not necessarily take the shortest distance between two points, it will travel whatever path takes the least amount of time. Sometimes, the path of least distance and the path of least time are the same. Other times, however, those two paths are not the same.
When light bounces off of a surface (such as a mirror) but otherwise travels through the same medium (such as air) throughout its journey, the path of least time is the same as the path of least distance. Because the speed of light through a single medium remains constant, the fastest path for light to travel will be the shortest path.
Consider light that starts at point A and bounces off of a mirror before traveling to point B. Any path that is not the shortest distance will take longer than the shortest path, due to the fact that time equals distance over velocity, and velocity remains constant through a single medium.
When light travels through different media, the path of least distance and the path of least time is no longer the same. Let’s consider the lifeguard problem as an analogy to understand why this is so.
Let’s say there’s a lifeguard on the beach. She sees a swimmer out in the water who needs help and may be drowning. The lifeguard needs to get to the swimmer as quickly as possible. She knows that she can run on the beach faster than she can swim through the water, so she wants to optimize her route to the swimmer to get to him as quickly as possible.
If the lifeguard takes a straight-line path to the swimmer, the path of least distance, she will spend too much time in the water. Because she’s slower in the water than on the beach, this will not be the fastest route. Alternatively, she could minimize the amount of distance she spends in the water, but this would cause her to spend too much time on land, which is also not an optimal route.
Depending on the lifeguard’s exact speeds in the land and in the water, her path of least time will be an optimization of more time on the beach, and less time in the water, without making the overall path longer than it needs to be.
When the speed of light changes throughout its journey from point A to point B, the light will bend in order to create the path of least time. We’ll see examples of this when we discuss refraction in a few moments.
Reflection is what happens when light bounces off of a surface. As we learned in lecture 27, selective reflection and absorption of different colors of light is what makes opaque objects look a certain color. When white light hits something blue, the blue light reflects (bounces) back to our eyes, and red and green light is absorbed by the object.
The law of reflection tells us how exactly each ray of light moves when it bounces off of a surface. Due to the principle of least time, and because the speed of light stays constant, the path of least distance will be equal to the path of least time. This leads to the law of reflection: the angle of reflection is equal to the angle of incidence.
When we talk about reflection and refraction, we measure angles with respect to the normal line. Wherever light is incident on a mirror, the normal line, at that point, is positioned at a right angle to the mirror’s surface. On a planar mirror this is a simple perpendicular line. When discussing angles, we use the Greek letter theta to indicate this quantity. The symbol theta I is used to discuss the incident angle, and theta r is used to discuss the reflected angle.
When light hits a mirror at a spot, the angle of incidence is measured between the light ray and the normal line. The angle of reflection is equal to this angle of incidence. Therefore, if you know the angle of incidence, you can determine the angle of reflection by using the law of reflection. They are equal!
As noted in lecture 27, selective reflection is how different objects appear to look different colors. If reflection is occurring, why can’t we see our reflection in objects that allow light to bounce off of them? The answer is that, while light always obeys the law of reflection, sometimes surfaces are rough enough that the light will bounce back in scattered directions. This type of reflection is known as diffuse reflection. Light that bounces off of a smooth, polished surface is known as specular reflection.
Before discussing how the law of reflection can be used to explain how different types of mirrors work, let’s discuss the concept of an image. When light reflects, the reflected light has properties that make it appear that those light rays were generated a particular spot. For example, when we look in a bathroom mirror and see our reflection, that reflection occurs at a point where the reflected rays of light appear to have been generated. This reflection of ourselves, or of other objects, is known as an image. When we look through mirrors, an image is said to be virtual when the image is behind the mirror and the image is said to be real when the image is in front of the mirror.
Let’s see how the law of reflection can be used to explain the images we see in different types of mirrors: planar mirrors, concave mirrors, and convex mirrors.
A planar mirror is a flat, smooth, reflective surface. You probably use one in the mornings and evenings when you brush your teeth and hair. These types of mirrors are extremely common in our daily lives.
Light reflects off a planar mirror abiding by the law of reflection: the angle of incidence is equal to the angle of reflection. We see an image in the mirror that appears behind the mirror. This comes about due to how light rays reflect off the mirror. If we trace the reflected rays of an object backward, they converge on points behind the mirror, creating a virtual image. Our eyes perceive the diverged light as coming from the virtual image. This virtual image appears upright and has the same size as the object. This is how we see our reflection in a planar mirror.
There are also curved mirrors. A concave mirror is a smooth reflective surface that’s curved inward. A curved mirror has a focal point, a place where all parallel rays will converge to a single point. The image that’s created in a concave mirror has to do with where an object is in relation to this focal point.
Let’s say the object is between the focal point and the mirror. Once again we can draw light rays and use the law of reflection to determine where those light rays will travel after bouncing off of the mirror. Our eyes perceive an image based on where these rays of light converge. In this case, they create a virtual image behind the mirror. The virtual image is upright and much larger than real life.
You may have used a concave mirror in this fashion if you’ve used a make-up or shaving mirror. This greatly magnifies the appearance of your face and makes it easier to apply make-up or shave.
As an object moves past the focal point, the image changes. Now, we can trace each ray of light and see that they converge on the same side of the mirror as the object, causing a real image. The term real image simply means that the image is created on the same side as the object, due to light rays converging rather than diverging. The real image generated in this case is upside-down and larger than the object.
It’s possible you’ve seen this effect if you’ve looked in a funhouse mirror. And if you step far enough away from a make-up or shaving mirror, you’ll notice that you will pass the focal point and go from being upright and magnified to upside-down and magnified!
A convex mirror is a mirror that’s curved outward. The focal point is behind the mirror. When we analyze light rays, we see that the object creates a virtual image behind the mirror that’s upright and smaller than the object.
There are many applications of convex mirrors in our lives. Perhaps you’ve seen them in a parking garage or other narrow space, to help you see what may be around a tight corner. I took this selfie at a parking garage in downtown Naperville.
Convex mirrors are also used as the side mirrors in our cars. They show us a slightly smaller version of what’s around us, allowing us to see an expanded view around the sides of our cars. But this is also why there’s usually a warning stating that “objects are closer than they appear.”
A “normal” mirror is simply a very smooth reflective metal (possibly silver) that’s been highly polished and covered with glass. If you touch the mirror, you’ll notice a gap between your finger and the reflection. This gap exists because of the presence of the glass protecting the polished metal surface.
Perhaps you’ve heard of a one-way mirror. A one-way mirror is simply a piece of glass that separates a dark area and a light area. These surfaces appear to look like a mirror if you’re on the light side of the glass, but they look like a window if you’re on the dark side of the glass. In fact, windows in buildings and homes also appear this way at night when it’s dark outside but interior lighting is used.
A one-way mirror isn’t really much of a mirror at all. On the light side, we can easily see our reflection because the light from the reflection outweighs the small amount of light passing through from the dark side of the glass. On the dark side, we simply see the light that transmits through from the bright side. There is too much transmitted light to enable somebody on the dark side of the glass to see their reflection. Instead, they see whatever is on the other side of the glass.
You can identify a one-way mirror by touching the glass. Because there is no metal reflecting surface, you’ll notice there is no gap between your finger and its reflection.
Refraction is a bending of light that occurs when light travels through different media. Because of the principle of least time, light will bend when it travels from air into some type of media (such as water or plastic) where the speed of light is slower than in free space. The extent to which the speed of light slows down is known as the index of refraction. The index of refraction has a symbol of the lowercase letter n. n is equal to the ratio of the speed of light in free space and the speed of light in that medium. In other words, n equals c divided by v. c is the speed of light in free space: 3 times ten to the 8 meters per second. V is the speed of light in that particular medium.
The index of refraction of a medium is an indication of how much light will bend when it enters that medium from free space. Something with a low index of refraction will bend light much less than something with a high index of refraction. For context, water has an index of refraction of 1.3. Diamond has a relatively high index of refraction of 2.4.
To quantify the bending of light, we look at the normal line. The normal line is drawn at a 90 degree angle to the medium. Light enters at an angle of incidence, which is measured with respect to the normal line. When light goes from a lower to higher index of refraction (for example, from air to glass), the angle of refraction will be smaller than the angle of incidence.
When light goes from a higher to a lower index of refraction (for example, from water to air), the angle of refraction will be larger than the angle of incidence.
The exact amount of bending can be explained by Snell’s law of refraction. Before I explain Snell’s law, let me reassure you that you will not be required to use this equation in class, as it contains trigonometry. So please don’t be afraid if the equation is confusing to you. Snell’s law of refraction states that n one times sine of theta one equals n two times sine of theta two. This means that the index of refraction of the first medium, times the sine of the angle of incidence, is equal to the index of refraction of the second medium, times the sine of the angle of refraction.
This bending of light explains some things you may have seen in your everyday life. For example, when a straw is placed in a glass of water, the refraction of light in the water causes the straw to look broken.
Refraction is also used to help our eyesight. Eyeglasses, not to mention lenses in general, use refraction of light through glass to focus light on the retina. I am nearsighted, which means light will naturally focus in front of my retina. My eyeglasses bend the light and cause it to focus on my retina instead.
Although Snell’s law of refraction seems to indicate that the amount of bending that occurs in a material is independent of wavelength, in fact, different wavelengths of light will bend more or less through different media. The index of refraction of a material is not just a single number, but is a function that varies based on the light wavelength. This fact can be used to split light into its constituent colors. This property is known as dispersion.
A prism splits white light into a rainbow due to dispersion. Each color of light bends different amounts. Red bends the least through glass, and violet the most. This difference in bending is what causes a rainbow to form. This also occurs in raindrops and is the physical cause of rainbows we see in the sky.
According to Snell’s law, light that travels from an object with a high index of refraction to a medium with a lower index of refraction will bend the refracted light outward. At a certain point, known as the critical angle, light that is incident on a high-to-low index of refraction interface will bend at a 90 degree angle, exactly along the interface. Light that is incident at angles greater than the critical angle will not refract at all, but will instead reflect off of the interface. This phenomenon is known as total internal reflection.
When I shine a laser pointer through a piece of shaped plastic, you can see the total internal reflection where the light reflects back into the plastic rather than bending outward back into the air.
Total internal reflection is used in fiber optics. Light rays are focused into a long fiber of glass with a laser, and total internal reflection causes those light rays to remain trapped inside of the fiber, allowing them to travel long distances as they carry telecommunications signals from one place to another.
Diamonds are cut with angles such that much of the light that travels into the diamond is trapped inside with total internal reflection, causing them to sparkle and shine.
If you’ve ever been under water and looked upward, total internal reflection is the reason why the surface of water from underneath tends to look shiny, somewhat like a mirror.
Just as mirrors cause reflected light to appear to have generated from a particular spot, lenses cause refracted light to appear to have been generated from a particular spot. Our eyes perceive the bent light as having come from that spot, known as an image. In the opposite terminology as mirrors, an image is said to be virtual when the image is on the same side of the lens as the object and the image is said to be real when the image is on the opposite side of the lens as the object.
A bi-concave lens causes parallel light waves to bend outward, or diverge. Bi-concave means that both sides of the lens are curved inward. We can determine that divergence occurs by applying Snell’s law of refraction at each interface between air and the lens. If we trace the diverged light rays backward, we can find a focal point. This is known as a virtual focal point because it’s in front of the lens.
An image viewed through a concave lens will be upright and smaller than the object that creates the image. It is known as a virtual image as it appears on the same side of the lens as the object.
A bi-convex lens causes parallel light waves to bend inward, or converge. Bi-convex means that both sides of the lens are curved outward. Snell’s law of refraction can be used to trace each ray of light and prove that the light converges to a focal point on the other side of the lens.
An image viewed through a convex lens, beyond the focal point, will be a real image as its rays trace to the other side of the lens. This image will be inverted and larger than the object.
An image viewed through a convex lens, between the focal point and the lens, will be a virtual image that is upright and magnified from the object.
Microscopes, telescopes, eyeglasses, magnifying glasses, and cameras all use lenses to magnify, focus, or create images of objects.
Thanks for taking the time to learn about reflection and refraction! Until next time, stay well.