Bendy, Bouncy, Beautiful! The Path Light Travels Bendy, Bouncy, Beautiful!

Part 1a: Reflection Basics Read this section for homework. Stop at Part 1b. We’ll do that part in class.

Reflection When light bounces off of something, it’s called reflection. Rule: The angle of incidence is equal to the angle of reflection

Angles and the “Normal) The angle of incidence and the angle of reflection are measured between the light ray and the “Normal.” The Normal is a line drawn perpendicular to the mirror’s surface. In the image below, the dashed line is the Normal and the solid line is the mirror.

Light beams and mirrors A bazillion rays of light bounce of a mirror at any given moment, from an infinite number of directions. However, the only rays that count are the ones that enter your eyes. So, we focus on one ray at a time.

Angle of Incidence The “incident ray” is the one ray that we are interested in as it comes TO the mirror. It is shown in yellow. The angle is measured between that ray and the Normal. It is shown in green.

Angle of Reflection The “reflected ray” is the one ray that we are interested in as it LEAVES the mirror. It is shown in orange. The angle is measured between that ray and the Normal. It is shown in green. It is the same angle as the angle of incidence.

Diffuse Reflection You can see things because light reflects off of them. You can see, say, a statue from pretty much any direction; this means that light is reflecting off it in every direction. This means that light from one direction will reflect in many directions because the surface is rough. This kind of reflection is called is called diffuse reflection. Most objects reflect light this way.

Even though the light shines from below, you can see the statue because light reflects back down to where you stand, not just upwards. The rough surface has “normals” in many directions.

Specular reflection If a surface is really smooth, like the surface of a mirror, then all incident rays from one direction are reflected in only one direction. This is why you can only see your reflection in a mirror if you are in front of it. This is called specular reflection.

Specular and diffuse reflection

The shiny spots are the result of specular reflection from the smooth surface of the water. The rough surface of the road yields diffuse reflection.

Light from the camera flash enters through the pupil Light from the camera flash enters through the pupil. It then reflects off the back of the eyeball, which is rich with blood vessels. The light then returns to the camera lens before the shutter clicks closed. In these photos, you can see what the back of someone’s eyeball looks like.

Virtual Images What does a dog do when it sees itself in a mirror for the first time? He goes up to the mirror to sniff, and goes behind it (if possible) to find that doggie in the window. The reflected dog image exists behind the mirror. Smart dog!

Drawing Ray Diagrams and locating virtual images Reflection Part 1b Drawing Ray Diagrams and locating virtual images

Images in Mirrors To understand reflected images from a mirror, you will need to determine where the normal is You also need to keep in mind that the image in a mirror is Virtual

Ray Diagrams for Mirrors Where is the normal for each of the mirror surfaces pictured at left? For the curved surfaces, it will be normal to the tangent at the point of incidence

Ray Diagrams for Mirrors Here are the tangents Draw in the normal lines

Ray Diagrams for Mirrors

Ray Diagrams for Mirrors

Ray Diagrams for Mirrors

Ray Diagrams for Mirrors Next, draw the reflected rays. Remember: the angle of incidence = the angle of reflection

Ray Diagrams for Mirrors

Viola!

Reflections from a mirror Now that you know the basics of reflection, You can draw ray diagrams of the images you see in mirrors, etc. The key to remember is this: the only rays you see are the ones entering your eye.

Let’s start with a flat mirror

Light from the top of the image…

Light from the middle of the image

Light from the bottom of the image

These are reflected rays

Where did they come from?

Where did they come from?

Where did they come from?

To draw the image, Start with the blank mirror and the object Draw the incident and reflected rays from the top of the object to the eye Remember: θincidence = θreflection. Draw the incident and reflected rays from the bottom of the object. (θ means “angle.”) Continue as needed in between

Start with light entering the eye from the top of the object

Then light from the bottom of the object

Where is that image? To understand this, you must think of the rays coming from each point on the image, to your eye.

Locating the image You can see that light enters the eye from different angles. What does the brain do with information that comes in from different angles? It thinks backwards!

Locating the image Isolate the rays coming to the eye and trace them backwards

Rays coming to the eyes

Trace backwards and fill in the image

A more accurate diagram

Since what you see in the mirror is small, it must be far away, right? The image in a flat mirror is behind the looking glass It is equidistant from the plane of the mirror as the object It is the same size as the object

Convex Mirrors Will you look bigger or smaller in a convex mirror? where would you would look to see light reflecting right back at you - so the angle of incidence is zero? That is, where would you look to find your eye?

Convex mirrors Notice that you have to look up to see your eye To see your toe, you would have to look down Project the thought lines - the image is magnified

Convex mirrors

Convex Mirrors Using the same technique, where would you have to look to find the reflection of your eye?

Convex mirrors Using the same technique, where would you have to look to find the reflection of your eye? Downward So, what is the image like?

Helpful Equations 1/f = 1/do + 1/di This is the lens equation It also works for converging mirrors (like concave ones) F is the focal length do is the object distance di is the image distance 1/f = 1/do + 1/di

Helpful Equations M = image height = h' M = -di M = i This is the magnification equation Here’s another way to find magnification And here’s the last one M = image height = h' object height h M = -di do = h' h M = i o h o i

Sample Problem 1 A 4.0-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Determine the image distance and the image size.

Identify knowns and unknowns di = do = f = h = h’ = A 4.0-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Determine the image distance and the image size.

Substitute into the equation di = do = f = h = h’ = 1/f = 1/do + 1/di M = -di = h' do = h

Answers: di = 22.8 cm h’ = -1.99 cm The negative value indicates what about the image? What if the di were a negative value? What would that mean about the image?

Determining magnification For a flat mirror, the M = 1

Determining magnification For a concave mirror, first look at the way the light reflects The rays converge; concave mirrors are convergent The image appears at the focal point Focal length = 1/2 Radius

Determining the magnification Is the image real or virtual? REAL, because the light rays converge Is the image erect or inverted? INVERTED; it’s just like a converging lens Focal length = 1/2 Radius if the mirror is spherical