Chapter 4 Basic Physics-Optics

PART II: Reflection, Refraction, Mirrors and Lenses
The Big Idea
Fermat’s Principle states that light will always take the path of least amount of time (not distance). This principle governs the paths light will take and explains the familiar phenomena of reflection, refraction, lenses and diffraction. Light rarely travels in a straight-line path. When photons interact with electrons in matter the time it takes for this interaction determines the path. For example, higher frequency blue light is refracted more than red because blue wavelengths interacts more frequently with electrons than red wavelengths and the path of least time is for blue to bend more then red in order to get out of this ‘slow’
area faster. The rainbows we see are a result of this. Fermat’s Principle explains the many fascinating phenomena of light from rainbows to sunsets to the haloes around the moon.
Key Concepts

• Fermat’s Principle makes the angle of incident light equal to the angle of reflected light. This is the law of reflection.
• When light travels from one type of material (like air) into another (like glass), the speed slows down due to interactions between photons and electrons. If the ray enters the material at an angle Fermat’s Principle dictates that the light also changes the direction of its motion. This is called refraction. See the figure shown to the right, which demonstrates the refraction a light ray experiences as it passes from air into a rectangular piece of glass and out again. Because light travels at slower than usual speed in transparent materials (due to constantly being absorbed and re-emitted), the light ray bends in order to get out of this material quicker and satisfy Fermat’s Principle. Note that this means that light doesn’t always travel in a straight line.
• When light is refracted its wavelength and speed change; however, its frequency remains the same as the frequency of the light source.
Key Applications

Total internal reflection occurs when light goes from a slow (high index of refraction) medium to a fast (low index of refraction) medium. With total internal reflection, light refracts so much it actually refracts back into the first medium. This is how fiber optic cables work: no light leaves the wire.
Lenses, made from curved pieces of glass, focus or de-focus light as it passes through. Lenses that focus light are called converging lenses, and these are the ones used to make telescopes and cameras. Lenses that de-focus light are called diverging lenses.
• Lenses can be used to make visual representations, called images.
Mirrors are made from highly reflective metal that is applied to a curved or flat piece of glass. Converging mirrors can be used to focus light – headlights, telescopes, satellite TV receivers, and solar cookers all rely on this principle. Like lenses, mirrors can create images.
• The focal length, f , of a lens or mirror is the distance from the surface of the lens or mirror to the place where the light is focused. This is called the focal point or focus. For diverging lenses or mirrors, the focal length is negative.
• When light rays converge in front of a mirror or behind a lens, a real image is formed. Real images are useful in that you can place photographic film at the physical location of the real image, expose the film to the light, and make a two-dimensional representation of the world, a photograph.

• When light rays diverge in front of a mirror or behind a lens, a virtual image is formed. A virtual image is a trick, like the person you see “behind” a mirror’s surface when you brush your teeth. Since virtual images aren’t actually “anywhere,” you can’t place photographic film anywhere to capture them.
• Real images are upside-down, or inverted. You can make a real image of an object by putting it farther from a mirror or lens than the focal length. Virtual images are typically right-side-up. You can make virtual images by moving the mirror or lens closer to the object than the focal length.
Key Equations

Light Problem Set
1. Consider the following table, which states the indices of refraction for a number of materials.
a. For which of these materials is the speed of light slowest?
b. Which two materials have the most similar indices of refraction?
c. What is the speed of light in cooking oil?

3. A certain light wave has a frequency of 4.29×1014 Hz. What is the wavelength of this wave in empty space? In water?
4. A light ray bounces off a fish in your aquarium. It travels through the water, into the glass side of the aquarium, and then into air. Draw a sketch of the situation, being careful to indicate how the light will change directions when it refracts at each interface. Include a brief discussion of why this occurs.
5. In the “disappearing test tube” demo, a test tube filled with vegetable oil vanishes when placed in a beaker full of the same oil. How is this possible? Would a diamond tube filled with water and placed in water have the same effect?
6. Imagine a thread of diamond wire immersed in water. Can such an object demonstrate total internal reflection? Draw a picture along with your calculations.

7. The figure above is immersed in water. Draw the light ray as it enters the Gas medium through its exit back into the water medium at the bottom. Be very careful drawing your light rays, making sure that it is clear when (and by how much) the angle is increasing, when decreasing and when staying the same. You may want to calculate the refracted angles to check your light ray drawings.
8. Here’s an example of the “flat mirror problem.” Marjan is looking at herself in the mirror. Assume that her eyes are 10 cm below the top of her head, and that she stands 180 cm tall. Calculate the minimum length flat mirror that Marjan would need to see her body from eye level all the way down to her feet. Sketch at least 3 ray traces from her eyes showing the topmost, bottommost, and middle rays. In the following five problems, you will do a careful ray tracing with a ruler (including the extrapolation of rays for virtual images). It is best if you can use different colors for the three different ray tracings. When sketching diverging rays, you should use dotted lines for the extrapolated lines behind a mirror or in front of a lens in order to produce the virtual image. When comparing measured distances and heights to calculated distances and heights, values within 10% are considered “good.” Use the following cheat sheet as your guide.


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