Sierzega/Ferri: Optics 4

Concave and Convex Mirrors 4.1 Observe and explain - a beam reflects from a concave mirror Shine the light from a laser pointer on a plane mirror and observe the reflected ray. Then shine it on a curved mirror, which is a piece of a sphere of radius R (concave). For two examples, the light reflects as shown in the illustration. Plane mirror

incident beam

incident beam

Concave mirror

R O

reflected beam

reflected beam

1. Explain this behavior in terms of the law of reflection. Note: The dashed line R passes through what would be the center O of the sphere from which the mirror was cut.

Vocabulary: Something that is concave bends inward. This is easy to remember, it's like a cave.

A perpendicular line from the center of a mirror is called the main axis:

main axis

main axis

Use your language brain and your picture brain! Consider these two highly technical definitions: Real image: If an optical device causes the light from one point on an object to reflect or bend so that it refocuses at some other point, then that point is said to be a real image of the object point. The optical device refocuses light from each point on the object to form a real image of that object. Virtual image: An optical device sometimes causes the light from one point on an object to reflect or bend so that it diverges and never refocuses. However, if your eye looks at this diverging light, it appears to diverge from some point other than the actual point on the object. This point is said to be the virtual image point of the object point (the word virtual means the light does not actually diverge from that point). The light reflected from the mirror appears to come from this virtual image.

Sierzega/Ferri: Optics 4 4.2 Predict and test - parallel beams incident upon a concave mirror (protractor required) Laser pointers are aimed parallel to the main axis of a concave mirror. Point O is the center of the sphere from which the mirror was cut. 1. Predict the path of the beams using the law of reflection. Work extra-carefully!

O

2. Try this mirror of a different curvature

O

3. What pattern do you see in these reflected beams?

4. Does this pattern appear for ALL incident beams?

Sierzega/Ferri: Optics 4 Definition: focal point Point the beams of the lasers parallel to the main axis of the mirror (a horizontal axis through the center of the mirror). After reflection, they all pass through the same point exactly in the middle between the mirror and the center of the sphere from which the mirror was cut. This point is called the focal point — the point through which rays parallel to the axis of the concave mirror pass after reflection from the mirror.

focal point

O center

main axis

4.3 Predict and test - Images in a concave mirror You can see an object because light rays diverge from the object in all directions and enter your eye. If the light rays diverge (or seem to diverge) from some other point, that is where you would see the object instead. Use the following instructions to help you predict where the image of a distant candle would appear in this concave mirror.

F focal point

O center

main axis

1. Draw two rays from the tip of the candle flame and show how they are reflected from the mirror. Hint: choose two rays that are easy to reflect. 2. Locate the point where these reflected rays come together. Are light rays diverging from this point also?

3. Draw one ray from the bottom of the candlestick and show how it is reflected from the mirror. Hint: choose one ray that is easy to reflect.

4. What would you expect to see if you placed a piece of white board near the place where these reflected rays converge?

Sierzega/Ferri: Optics 4

4.4 Observe and explain- a beam reflects from a convex mirror Shine the light from a laser pointer on a curved mirror, which is a piece of a sphere of radius R (convex). The light reflects as shown in the illustration. incident beam

Convex mirror reflected beam

R O

1. Explain this behavior in terms of the law of reflection.

4.5 Predict and test - reflections from a convex mirror 1. Predict the path of rays reflected from a convex mirror if the incident rays are parallel to the mirror's main axis.

convex mirror

main axis

O center

2. Identify a point where the rays meet after reflection, or alternatively, a point from which all of the reflected rays seem to originate.

3. Does a convex mirror have a focal point? If so, where?

Sierzega/Ferri: Optics 4 4.6 Predict and test - images of an object in a concave mirror 1. Locate the image of the candle when the candle is located at distance s > O

f

s

O

Describe the image. Is it upright or inverted? Enlarged or reduced? Real or virtual? 2. Locate the image of the candle when the candle is located at distance f < s < O.

s

f

O

Describe the image. Is it upright or inverted? Enlarged or reduced? Real or virtual? 3. Locate the image of the candle when the candle is located at distance s < f.

s

f

O

Describe the image. Is it upright or inverted? Enlarged or reduced? Real or virtual?

Sierzega/Ferri: Optics 4 4.7 Summarize and review - real and virtual images Concave Mirror: A concave mirror is capable of forming both types of image, depending on where the object is located. In this example, observers would agree that the reflected light rays seem to be coming from a point behind the mirror. When reflected light rays are not actually coming from the spot where the image is seen, we call it a virtual image. virtual image

f

In the example below, observers would agree that the reflected light rays diverge from a point in front of the mirror. In this case, the light rays that reach the viewer's eye are actually coming from the location of the image. This is called a real image.

f real image

1. What type of image is formed by a plane mirror? Draw a ray diagram and explain.

2. What type of image is formed by a convex mirror? Draw a ray diagram and explain.