7.4.2: Explorations

Exploration 1: Image Formation

An object is placed in front of a converging lens outside of the focal point. Restart.

1. Draw a ray diagram to locate the image. You can check your answer below.
2. View object and image. Now consider a point at the top of the object. Light must leave this point and travel in all directions (otherwise everyone in a room would not be able to view an object at the same time). Draw the rays that leave the top of the object and travel through the lens. Once you have your drawing, check your answer by clicking on the link below. Were you correct? If not, why?
3. Initialize part (c) and then move the light source to different points on the object. As you drag the point source up and down, notice that the rays from one point on the object all converge at the same point on the image. Are all the rays leaving a point on the object blocked if half of the lens is cut off? Add a screen. How would the image appear if the top half of the lens were blocked?

Exploration authored by Melissa Dancy and Anne J. Cox.

Exploration 2: 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 (position is given in meters). The animation shows an object arrow, a lens, and pink dots to show the focal point of the lens. Restart.

1. Two point sources are attached to the object in the animation. Move the object and notice where the rays from the point sources converge. In order to sketch a diagram of the object, the lens, and the approximate position of the image, you need to know where the light from these sources (from the object) converges. As you move the object around, what do you notice about the rays that are parallel to the principal axis (either before entering the lens or after leaving the lens)? Why do they always cross the axis at the same place?
2. 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 (sometimes called principal rays) to sketch a ray diagram. Change to the "ray diagram" view. Describe the three rays (compare them to the list in your textbook, if needed). Which one goes from the object through the lens and then through the focal point? Which one seems to be undeflected as it goes through the lens? Which one goes through the focal point (on the object side) and then through the lens?
3. Look at a diverging lens with a point source. Try sketching a ray diagram for a diverging lens. Check it by looking at the ray diagram.

Exploration authored by Anne J. Cox.

Exploration 3: Moving a Lens

In this animation the lens is movable, but the object is not (position is given in meters). Initially, you have a lens of an unknown focal length (that you cannot adjust using the slider). Restart.

1. What are the object and image distances for the lens? Find the focal length of the lens.
2. There is another spot where you can put the lens that will give an image at the same position (on the blue screen). Move the lens until an image appears at the same spot (on the blue screen). What are the object and image distances this time?
3. For a given distance between an object and a screen, develop an equation for the two spots where you can place a lens to get a clear image on the screen. Verify your expression for a lens with an adjustable focal length (use the slider to change the focal length). Note that when you click or drag this lens, the focal length (f.l.) appears on the screen.

Exploration authored by Anne J. Cox.

Exploration 4: What is Behind the Curtain?

A dragable source of light is shown along with an optical element that has been hidden behind a pink curtain (position is given in meters). Restart.

1. What is behind the curtain? Do not read the rest of the question until you have answered this part.
2. AFTER you have determined what is behind the curtain, remove the curtain to see if you were right. Surprised?
3. Most students predict there is a converging lens with a focal length around \(1\text{ m}\) behind the curtain. Without removing the curtain, could you have known this prediction was incorrect?
4. Find the focal length of the individual lenses. Remember that when an object sits at the focal point of a lens, the light exits the lens parallel to the axis, and when light enters a lens parallel, it converges at the focal point. So, move the object to the focal point of the first lens, and the light should converge at the focal point of the second lens.

Exploration authored by Melissa Dancy.

Exploration 5: Lens Maker's Equation

Light rays from a beam source, initially in air, are incident on a material of different index of refraction (position is given in centimeters). You can change the curvature of the surface of the material as well as the index of refraction. Restart.

1. Build a plano-convex lens. Decrease the radius of curvature of the left side while keeping the right at \(30\text{ cm}\). As you decrease the radius of curvature, what happens to the beam? When the curvature of the left side is \(1\text{ cm}\), where is the point at which all the rays converge? How far is the point where the rays converge from the center of the "lens" you are making? This is the focal point of the lens.
2. What happens if you keep the left side essentially flat (radius \(= 30\text{ cm}\)) and decrease the radius of curvature of the right side? What is the focal point when this radius is \(1\text{ cm}\)? What happens to the focal point if you increase the index of refraction of the material? What happens if you decrease it?
3. Build a double-convex lens. Decrease the radius of curvature of both sides of the lens. What is the focal point when the radius of curvature is \(1\text{ cm}\) for both sides? How does the focal point change with a different index of refraction?
4. Analytically, the focal length is described by the lens maker's equation: \(1/f = (n - 1)(1/R_{1} + 1/R_{2})\), where \(R_{1}\) and \(R_{2}\) are the radii of curvature, \(f\) is the focal length, and \(n\) is the index of refraction. Verify that your earlier measurements are consistent with this equation.
5. For lenses made from glass (\(n = 1.5\)), show that the radius of curvature of a double-convex lens (where the radii of both sides is the same) is equal to the focal length.

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