7.2.2: Explorations

Last updated

Mar 8, 2021
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- 7.2.1: Illustrations
- 7.2.3: Problems

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Exploration 1: Image in a Flat Mirror

A bear stands in front of a plane mirror that is hanging on a wall. A point source of light is located near the mirror. You can drag this source to any location and can change the angle of its rays by click-dragging on the hotspot (position is given in meters and angle is given in degrees). Restart.

At what point on the mirror must the bear look in order to see her feet? For simplicity and ease, assume the bear's eye is located at the tip of her nose.
Move the bear to the position $x = 1.0\text{ m}$ . If the bear looks at the same spot in the mirror found in (a), what will she see? Does this imply that she is able to see more, less, or the same amount of her body in the mirror when she moves away from the mirror?
In terms of the bear's height, how long must the mirror be for her to see her entire body?

Exploration authored by Melissa Dancy.

Exploration 2: Looking at Curved Mirrors

What is the difference between a real and a virtual image? What does your eye see when it looks into a mirror (position is given in meters and angle is given in degrees)? Restart.

Drag the object back and forth. In this animation when the image is on the left of the mirror it is a real image, but when it is on the right it is a virtual image. Why?
Place the object so that the image is to the right of the mirror (a virtual image). If your eye is where the eye is in the diagram, where does your eye/brain think the light is coming from? Because you think light travels in a straight line, when light diverges from a point, your brain assumes that the point it diverges from (the image point) is where the light originated. So, for a virtual image like this, your eye/brain sees an image and thinks it is behind the mirror.
What about a real image? Place the object at some point so that the image forms somewhere in front of the eye. Where does the eye think the light comes from? What does the eye see? (Is the image upright or inverted, bigger or smaller than the object?) What if the image point is beyond the eye? What would that look like? (Notice that for this case the light doesn't seem to have a convergence point so you'd see a blurry image.)
In which case is the light actually traveling through the image point? For real images, the light actually travels through the image point. If you put up a screen at the point where the rays cross, then a real image can be formed on the screen, whereas if you put up a screen at the point of a virtual image, you won't see anything on the screen (the screen is behind the mirror).

Exploration by Anne J. Cox.

Exploration 3: Ray Diagrams

You will often use ray diagrams in order to determine where an image of an object will be, whether it will be real or virtual, and whether it will be inverted or upright. The animation shows an object arrow, a mirror, and a pink dot to show the focal point of the mirror. You can move the object using the slider (position is given in meters). Restart.

One point source is attached to the object in the animation. Move the object and notice where the light from the point source converges. Move the point source up and down and notice where on the image the light converges. In order to sketch a diagram of the object, in addition to the lens and the approximate position of the image, you need to know where the light from every point on the object converges. Instead of trying to draw a large number of the rays from many points on the object, we generally use three rays from the tip of the object.
As you move the object (with the slider) or move the point source, there is a ray that always passes through the focal point. Describe that ray. This is a ray generally included in a ray diagram.
Now switch to the "ray diagram" view. Describe the other two rays (compare them to the list in your textbook, if needed). As you move the object, describe what stays the same for each ray even when the object is in a different position and the image is changing position and size.
Move the object to a position between the focal point and the mirror. Compare the object with point source and ray diagram views.

Exploration by Anne J. Cox.

Exploration 4: Focal Point and Image Point

In the animation you have the option of adding both a parallel beam source and a point source of light as well as mirrors (position is given in meters). Whenever you add a mirror, all the light sources will be cleared off the screen. Restart.

First, add a concave mirror and then add a parallel beam source. Where do the light rays converge? This is the focal point of the mirror.
Now, add a point source of light (move the parallel beam source to the right of the mirror). Where do the rays converge? Is it at the focal point?
Move the point source around. What happens to the point where the rays converge?
Now add an object. Put the object and point source at the same place. Where is the image in relation to the point where the rays converge? What is the difference between the focal point and an image point?
What happens when you move the object to the focal point of the mirror? Why?
What happens when the object is between the focal point of the mirror and the mirror itself?
What is the difference between images when the object is inside the focal point or outside the focal point? (If you find that the screen is too cluttered to see what is happening, you can clear the screen and add only a concave mirror and an object.)
Which images are real images and which ones are virtual? How can you tell?
Clear the screen and add a convex mirror and an object. Describe (and explain) the image formed.

Exploration authored by Anne J. Cox.

Exploration 5: Convex Mirrors, Focal Point, and Radius of Curvature

You can add a parallel beam source, a point source, and an object (position is given in meters and angle is given in degrees). How do you find the focal point of a convex mirror? Restart.

First, add a parallel beam source. Move it around so that one of the beams leaves the mirror parallel to the axis. This beam acts as if it came from the focal point. Why? So, to find the focal point, you need to extend the original path of this beam to the right side of the mirror. The easiest way is to use the "protractor" to click-drag an angle measure. You can move the protractor around as well as click-dragging to change the angle. If the mirror were not there, where would the original beam hit: the blue, green, red, or pink dot?
Now, move the parallel beam source until one of the beams bounces back on itself. This time where does an extension of the incoming beam originate: the blue, green, red, or pink dot? This is the radius of curvature of the mirror (radius of the circle that the lens would make). The radius of curvature should be twice the focal length.
Add a point source. How would you devise a method to determine the focal point of the mirror with a point source? Describe your method.
Finally, add an object and develop a method to determine the focal point with an object source.

Exploration authored by Anne J. Cox

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.

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Exploration 1: Image in a Flat Mirror

Exploration 2: Looking at Curved Mirrors

Exploration 3: Ray Diagrams

Exploration 4: Focal Point and Image Point

Exploration 5: Convex Mirrors, Focal Point, and Radius of Curvature

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