# PHYS 160 Astronomy. When analyzing light s behavior in a mirror or lens, it is helpful to use a technique called ray tracing.

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1 Optics Introduction In this lab, we will be exploring several properties of light including diffraction, reflection, geometric optics, and interference. There are two sections to this lab and they may be done in any order. I. Mirrors and Lenses Mirrors and lenses come in all shapes and sizes. You are probably most experienced with a standard, flat mirror. Mirrors can also be formed into different shapes like parabolic, hyperbolic, or spherical. Lenses are grouped into converging and diverging lenses. In this lab we will work with a variety of shaped mirrors and lenses. A spherical mirror, with radius of curvature R, is one that uses a portion of a mirrored spherical surface. If the incident light (the light moving towards the mirror) approaches the inside of the curve, the mirror is said to be concave. If the incident light approaches the mirror on the outside of the curve, the mirror is said to be convex. Concave mirrors cause the light rays to converge (come together), while convex mirrors cause light rays to diverge (spread apart). If the reflected light rays converge to a single point, the image formed is called real. An image is real if you can place a screen at the position of the image and see the image on the screen. In general, if the image is magnified, it can be projected and therefore is real. If the light rays diverge from the mirror, the image is said to be virtual. A virtual image would not appear on a screen if it were placed at the location of the image. For example, think about a standard flat mirror. The image that appears when you stand in front appears to be behind the mirror. If you placed a screen behind the flat mirror, your image would not be projected on the screen. Therefore it is a virtual image. With virtual images, the light rays do not actually reach the position of the image. Instead, the eye and brain interpolate the image position from the direction of diverging light rays. When analyzing light s behavior in a mirror or lens, it is helpful to use a technique called ray tracing. The rules for ray tracing are: 1. A ray passing through the center of the lens is not deviated. 2. A ray parallel to the axis is refracted so that it passes through (or extends through) the focal point, F. 3. A ray that passes from the object, through the focal point, and then to the mirror or lens will emerge from the mirror or lens parallel to the axis. 4. The image will appear at the intersection of 2 or more of these lines. See Figure 1-3 for examples of ray tracing for spherical mirrors and lenses. Page 1

2 Figure 1 Concave mirror, real image Figure 2 Convex mirror, virtual image Figure 3: Various lens ray diagrams. Some important variables when dealing with lenses and mirrors are: p q f R M The distance between the object and the lens/mirror The distance between the image and the lens/mirror The distance between the lens/mirror and the focal point The radius of curvature of a lens/mirror Magnification Page 2

3 The location of an image is given by the equation: = p q R (1) It is usually more convenient to use a focal length instead of the radius of curvature. For curved surfaces, the focal length is half of the radius of curvature. To measure the focal length of a mirror, send parallel light rays towards the mirror and see where the reflected rays meet. See Figure 4 for an example. R f = 2 (2) Figure 4 Combining equations (1) and (2), we get: = p q f (3) To use these equations, you must be very careful about signs. The standard sign convention is: The numerical value of p is almost always positive. For this lab, assume p>0. For mirrors, the numerical value of q is positive if the image is in front of a mirror (real), and negative if the image is behind the mirror (virtual). For lenses, q is positive if the image is not on the same side as the object (real), and negative if the image is on the same side as the object (virtual). For mirrors, f>0 for concave and f<0 for convex. For lenses, f>0 for convergent and f<0 for divergent. The image qualities can be described by a quantity called magnification. Once q is found using Equation 3, magnification is calculated: M q = p (4) Page 3

4 Magnification describes the image in the following ways: If M is positive, the image will appear upright. If M is negative, the image will appear upside-down. M is the ratio of the image height (h ) and the object height (h ). q h' M = =. p h o If M is equal to 1, then the image is the same size as the object. o If M>1, then the image is larger than the object. o If M<1, then the image is smaller than the object. For example, If M=+2, then the image is twice as tall as the object and upright. If M=-1/3, then the object is three times taller than the image and the image is upside-down. A. Procedure: Ray Tracing At this station, you will find a light source with several aperture shapes as well as several glass shapes. 1. Place the aperture with five slits in the light source. Turn on the light. 2. Place the converging lens in the light path. Move the lens until you can clearly see the light converging to a focal point. Draw the light path. Trace the shape of the lens on the paper. Measure the focal length. 3. Repeat for the diverging lens. 4. Repeat for the half-circle lens. Rotate the lens until you can clearly see at least one total internal reflection. 5. Place the converging and diverging lenses together so they fit together like puzzle pieces. Place the two lenses (pressed together) in the light path. Draw the light path. 6. Replace the 5-slit aperture with the single wide slit aperture. Place a prism in the light path. Rotate the prism until a rainbow appears on a piece of paper (held by a lab partner). Draw a sketch and explain why the white light of the source is separated into colors by the prism. B. Procedure: Lenses This set-up includes an optics rail, several holders, a light source that produces an arrow pattern, several lenses. 1. Place a converging lens in the mirror holder. The lens box should be marked with its focal length, f. Find a place where the image is sharply focused on a paper screen. Make sure that the lens is at least 20 cm away from the light source. Describe the image (circle correct answer): The image is: Real Virtual Upright Upside-down Smaller than object Larger than object Page 4

5 Measure the distances p and q. p= (cm) q= (cm) Plug your numbers into equation 3. Calculate the focal length of the mirror, f. Calculated f (cm) The lens focal length should be printed on lens box. Compare your calculated value of focal length to the value on the box. Calculate the magnification using equation 4. M= Measure the height of the image (h ) and the height of the object (h). Compute h /h. Does it agree with you value of M? h /h= 2. Build a refracting telescope: a. Replace the arrow light source with the post that has a small word taped to the end. b. Place the converging lens from box 1 at a distance of 45 cm from the post. Place the converging lens from box 2 at a distance of approximately 100 cm from the post. Look through both lenses, towards the post. Adjust the rear lens until the word is in sharp focus. Describe the image (inverted/upright, magnified, etc). Page 5

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