PHYSICS 106. Assignment #10 Due by 10 pm Tuesday April 13, DISCUSSION SECTION: [ ] D1 W 9 am [ ] D2 W 10 am [ ] HS W 10 am

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1 PHYSICS 106 Assignment #10 Due by 10 pm Tuesday April 13, 010 NAME: DISCUSSION SECTION: [ ] D1 W 9 am [ ] D W 10 am [ ] HS W 10 am [ ] D3 W 11 am [ ] D4 W 1 pm [ ] D5 W 1 pm (Sophie) [ ] D6 W 1 pm (Nima) [ ] D7 W pm [ ] D8 W 7 pm [ ] D9 F 9 am [ ] E1 F 10 am [ ] E F 11 am [ ] E3 F 1 pm [ ] E4 + E5 F 1 pm PLEASE CHECK OFF YOUR DISCUSSION SECTION ABOVE! INSTRUCTIONS: 1. Please include appropriate units with all numerical answers.. Please show all steps in your solutions! If you need more space for calculations, use the back of the page preceding the question. For example, calculations for problem 3 should be done on the back of the page containing question. You must show correct work to receive full credit. Support your answers with brief written explanations and/or arguments based on equations. 3. Indicate clearly which part of your solution is the final answer. 4. Try answering these problems, as much as possible, without a calculator and using only the equation sheet to help you. This will help you prepare for the test. 5. Grading scheme for each problem: grades for each part are integers only no half points. Please do your draft work of the assignment elsewhere, and copy your work over neatly when you hand in the assignment. The graders will deduct points for work that is difficult to follow. Angle (θ) sin(θ) cos(θ) tanθ = sinθ cosθ Problem 1: Problem : Problem 3: Problem 4: Problem 5: TOTAL:

2 PROBLEM 1 10 points The figure in part (a) shows a periscope, such as that used by submarine captains to see what is at the surface of the water, or by spectators at golf tournaments to see over the heads of people standing in front. Two parallel plane mirrors, each placed at 45 to the vertical, are used to make the periscope. [ points] (a) On the figure, show a location where your eye could be placed to view an image of the object through the periscope. To support your answer, show the path of one ray of light that leaves the object, reflects off both mirrors, and enters your eye. [1 point] (b) The second figure shows possible locations for the image of the object that is created by mirror 1. Which point is the correct location of that first image? [ ] A [ ] B [ ] C [ ] D [ ] E [ points] (c) Sketch a ray diagram on the second figure to justify your answer to (b) you need to show at least two rays. [1 point] (d) The third figure (identical to the second) also shows possible locations for the image that is created by mirror. Treat the image created by mirror 1 as the object for mirror. Which point is the correct location of this second image (this is the image you see when you look in the periscope)? [ ] F [ ] G [ ] H [ ] I [ points] (e) Sketch a ray diagram on the third figure to justify your answer to (d) you need to show at least two rays. [ points] (f) When you look at an object through the periscope, is the image you see the same horizontal distance away from you as the object is? [ ] Yes [ ] No, the image is closer to you, horizontally, than the object is [ ] No, the image is always twice as far away from you, horizontally, as the object is [ ] No, the image is farther from you, horizontally, than the object is by a distance equal to the vertical distance between the centers of the two mirrors

3 PROBLEM 10 points You have a concave mirror with focal length, f = +5 cm and an object that is cm tall. [1 point] (a) Draw a ray diagram to find the image when the object is placed at a distance of 3f in front of the mirror. [1 point] (b) Draw a ray diagram to find the image when the object is placed at a distance of f in front of the mirror. [1 point] (c) Draw a ray diagram to find the image when the object is placed at a distance of 3f/ in front of the mirror.

4 [1 point] (d) Draw a ray diagram to find the image when the object is placed at a distance of f in front of the mirror. [1 point] (e) Draw a ray diagram to find the image when the object is placed at a distance of f/ in front of the mirror. [5 points] (f) Based on your answers in parts (a)-(e), complete the following table for the characteristics of images formed by a concave mirror. In the table, R is the radius of curvature of the mirror. d o > R d o = R R > d o > f d o = f d o < f Virtual or real Upright or inverted Image size (larger, smaller, or the same size as the object)

5 PROBLEM 3 10 points A lamp emitting red light is placed at the bottom of a tank of liquid with depth H and index of refraction n (for red light). Above the liquid is air, which has an index of refraction of 1. On the surface of the liquid above the light, an observer sees a bright circle with radius, R. [ points] (a) Explain why the observer sees a bright circle on the surface. [3 points] (b) Find an expression for the radius, R, of the bright circle a person observes on the surface of the liquid, in terms of the variables given above. [ points] (c) If a beam of light travels directly from the lamp to the surface at point A, along the dashed line shown in the figure, [ ] it refracts in the air and goes away infinitely far from the lamp [ ] it goes away infinitely far from the lamp along the surface of the liquid [ ] it reflects back into the liquid [3 points] (d) If the lamp is adjusted to emit green light instead, the radius of the bright circle [ ] decreases [ ] stays the same [ ] increases Briefly justify your choice.

6 PROBLEM 4 10 points A lens produces an image that is one-quarter of the size of the object when the object is located 60.0 cm in front of the lens. The lens is made from glass, and we have the usual situation of the lens and object being surrounded by air. Our goal here is to find the type of lens, the focal length of the lens, and the image distance. There are two possible solutions! We will explore both. (a) [ points] What kind of lens is this? [ ] concave only concave lenses produce images larger than the object [ ] convex only convex lenses produce images larger than the object [ ] both! This is why there are two solutions one with each kind of lens. (b) [ points] For one solution, the image is real. For this solution, find the image distance, and find the focal length of the lens. (c) [ points] Draw a ray diagram (to scale) for the situation described in part (b). (d) [ points] For the second solution, the image is virtual. For this solution, find the image distance, and find the focal length of the lens. (e) [ points] Draw a ray diagram (to scale) for the situation described in part (d).

7 PROBLEM 5 10 points (a) [ points] Draw a ray diagram (to scale) for the situation of an object placed 8.0 cm in front of a lens that has a focal length of +0 cm. [ points] (b) What kind of image is formed in this case? [ ] real and upright [ ] real and inverted [ ] virtual and upright [ ] virtual and inverted [ points] (c) On the picture above, show a location where you could position your eye so as to see the image created by the lens. [1 point] (d) If the object in part (a) is moved a little closer to the lens, what happens to the image? [ ] The image moves closer to the lens, and gets smaller [ ] The image moves closer to the lens, and gets larger [ ] The image moves farther from the lens, and gets smaller [ ] The image moves farther from the lens, and gets larger [1 point] (e) Justify your answer to (d) with a diagram.

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9 [1 point] (f) In this situation, if the object is moved to the location of the image, where will the image be? [ ] at the original location of the object [ ] even closer to the lens than it was before [ ] farther from the lens than it was before [ ] on the other side of the lens from where it was before [1 point] (g) Justify your answer to (f) with a diagram.