Physics - Final Lab (optics)

Ryan Thomas 5/25/08 A. P. Physics

Key: Sure, Unsure, Really Unsure, Data Missing

Optics Lab Report Experiment 1: Color Addition Table 1.1 – Results of Color Addition COLORS ADDED RESULTING COLOR red + blue + green White red + blue Fuchsia red + green Yellow green + blue Cyan Table 1.2 – Results of Reflection Off Colored Paper COLOR OF PAPER COLOR OF COLOR OF PAPER IN IN WHITE LIGHT LIGHT RAY COLORED LIGHT Red Fuchsia Green Green/Cyan Blue Blue Deep Blue Red Red/Orange Green Green/Yellow Yellow Blue Blue/Green Red Deep Red Green Yellow/Green Red Blue Fuchsia Red Orange Green Bright Green Green Blue Blue/Cyan Experiment 2: Prism Procedural Questions: 3a) What colors are seen and in what order are they? (In Order) Violet, Indigo, Blue, Green, Yellow, Orange, and Red; Technically, all the colors in the visible spectrum, beginning with Violet and ending with Red. 3b) Which color is refracted at the largest angle? Violet 3c) According to Snell’s Law and the information given about the frequency dependence of the index of refraction for Acrylic, which color is predicted to refract at the largest angle? Violet

4) Do the colored rays emerge from the rhombus parallel to each other? Why or why not? No. The waves that we see as colored light each have different frequencies, and therefore different indexes of refraction in the acrylic material; this causes all three waves to refract at different angles from each other as they collide with the prism’s walls. They therefore exit also at separate angles, and thus are not parallel, by definition. Experiment 3: Reflection – Plane and Curved Mirrors Table 3.1 - Plane Mirror Results Angle of Incidence Angle of Reflection 45 45 30 30 15 15 Table 3.2 – Cylindrical Mirror Results Concave Mirror Focal Length 2 9/16 inches Radius of Curvature 5 1/8 inches using Compass

Convex Mirror 2 9/16 inches 5 1/8 inches

Questions – Part I: 1) What is the relationship between the angle of incidence and the angle of reflection? They are exactly the same. 2) Are the three colored rays reversed left-to-right by the plane mirror? Yes, like so:

Questions – Part II: 1) What is the relationship between the focal length of a cylindrical mirror and its radius of curvature? Do your results confirm your answer? F = ½ R; Yes, as 2 9/16 inches = (1/2)(5 1/8 inches) 2) What is the radius of curvature of a plane mirror? Infinite; incoming parallel rays of light will never focus, making the focal length infinite, and since F = ½ R, the radius of curvature is therefore (2)(infinity), which is still infinity, just as (2)(0) is still 0. Experiment 4 – Snell’s Law Table 4.1 – Data and Results Angle of Incidence Angle of Refraction 22.5° 17° 74° 45° 44° 27° Average index of refraction Percent deviation from accepted value

n rhombus 1.31 1.35 1.53 1.40 6 2/3 %

Question: What is the angle of the ray that leaves the rhombus relative to the ray that enters the rhombus? 0°; the rays are parallel. Experiment 5 –Total Internal Reflection Procedural Data: - Measured Critical Angle: 43° - Theoretical Critical Angle: 41.81° - Percent Difference Between Critical Angle: 7% Questions: 1) How does the brightness of the internally reflected ray change when the incident angle changes from less than θc to greater than θc? The brightness increases as the angle passes the critical threshold. 2) Is the critical angle greater for red light or violet light? What does this tell you about the index of refraction? The critical angle is greater for red light. This means that red light must have a greater index of refraction than violet light in acrylic, as θc and n are directly proportional.

Experiment 6: Refraction – Convex and Concave Lenses Table 6.1 - Results Focal Length

Convex Lens 5 ¾ inches

Concave Lens 5 ½ inches

Procedural Questions: 6) No; one is 5 ¼ inches and the other is 6 inches 7) All the rays seem to focus at the same point. The two lens system focuses the rays closer to the source than they would have focused with only the single lens. This is to be expected; each lens bends rays to a sharper and sharper angle, decreasing the distance until they finally converge. Experiment 8: Apparent Depth Procedural Data – Part I: - Apparent Depth: 13/16 inches - Apparent Thickness: 1 3/8 inches - Calculated Index of Refraction: n = t/d = 1.375/0.8125 = 1.7 - Percent Difference (Of accepted value, between accepted and calculated values): 13% Procedural Data – Part II: - Distance “x”: ½ inches - Calculated Index of Refraction: n = t/d = 1.375/.5 = 2.75 - Percent Difference (Of accepted value, between accepted and calculated values): 83% Experiment 9: Focal Length of a Thin Lens Table 9.1 Object Distance 1 12.6 cm 2 88.8 cm 3 16 cm 4 32.9 cm 5 14.2 cm 6 47.1 cm 7 57.5 cm 8 13.6 cm 9 13.3 cm 10 68.2 cm 11 78.5 cm 12 13 cm

Image Distance 87.4 cm 11.2 cm 32 cm 15.1 cm 45.8 cm 12.9 cm 12.5 cm 56.4 cm 67.7 cm 11.8 cm 11.5 cm 77 cm

Image Size (Magnification) -7x -0.13x

NO DATA TO RECORD HERE

1/do 0.079 0.011 0.065 0.030 0.070 0.021 0.017 0.074 0.075 0.015 0.013 0.077

1/di 0.011 0.089 0.031 0.066 0.022 0.078 0.080 0.018 0.015 0.085 0.087 0.013

Procedural Data: - Focal Length (Solved using limits): 10 cm - X-intercept: 0.089 - Y-intercept: 0.101 - F Average: 10.57 cm - Percent Difference: 5.7% Questions: 1) Is the image formed by the lens erect or inverted? The image is always inverted. 2) Is the image real or virtual? How do you know? The image is real, as it can be, and is, projected onto a screen. 3) Explain why, for a given screen-object distance, there are two positions where the image is in focus. The image focuses whenever 1/di + 1/do equals a specific number (1/f); this can happen twice for a given screen-object distance because there will be two points at which the lens can be placed where such a ratio is achieved: once where di is greater and once where do is greater. The concept here is like that of the fact that you can be one unit away from zero on a number line twice: once in the positive direction, and once in the negative direction. 4) Why is the magnification negative? The magnification is negative because the image is always inverted, which is denoted with negative magnification. The common misconception that makes such a magnification confusing is that the negative sign denotes a negative size, not a negative direction. Experiment 10: Telescope Table 10.1 - Results Position of Objective Lens (200 mm) Position of Eyepiece Lens (100 mm) Position of Screen Observed Magnification do1 di1 do2 di2 Calculated Magnification Percent Difference Questions: 1) Is the image inverted or erect? 2) Is the image seen through the telescope real or virtual?