5. [6 points total] In some bathrooms you may find parallel mirrors facing each other on...

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5. [6 points total] In some bathrooms you may find parallel mirrors facing each other on opposite walls, as shown in the figure at right. The distance between the two mirrors is H and the person is standing a distance d in front of the front mirror. a) 10.5 points] On the diagram, draw the image of the person formed by the front mirror and label it "A". b) [0.5 points] Draw the image of this image formed by the back mirror and label it "B" - assume that the mirrors are perfectly parallel to each other. c) [0.5 points] Draw the image of image B formed by the front mirror and label it "C". d) [1 point] Of the images you drew, which could be seen by the person looking into the front mirror? Explain your reasoning. front mirror Person back mirror e) [2 points] Determine an expression (in terms of d and H) for the distance between the person and image C. If the person takes a step back so that they are twice the distance from the front mirror, does the distance to image C double, increase but not double, halve, decrease but not halve, or stay the same? Show your work and explain your reasoning. f) [1.5 points] Say that the mirrors are not exactly parallel but are at a slight angle to each other- as is shown in the diagram. How does this affect what is seen by the person looking into the front mirror? Explain your reasoning. As part of your explanation, remake the diagram (either in another color, or with clear labeling) showing the series of images in these slightly tilted mirrors. 5. [6 points total] In some bathrooms you may find parallel mirrors facing each other on opposite walls, as shown in the figure at right. The distance between the two mirrors is H and the person is standing a distance d in front of the front mirror. a) 10.5 points] On the diagram, draw the image of the person formed by the front mirror and label it "A". b) [0.5 points] Draw the image of this image formed by the back mirror and label it "B" - assume that the mirrors are perfectly parallel to each other. c) [0.5 points] Draw the image of image B formed by the front mirror and label it "C". d) [1 point] Of the images you drew, which could be seen by the person looking into the front mirror? Explain your reasoning. front mirror Person back mirror e) [2 points] Determine an expression (in terms of d and H) for the distance between the person and image C. If the person takes a step back so that they are twice the distance from the front mirror, does the distance to image C double, increase but not double, halve, decrease but not halve, or stay the same? Show your work and explain your reasoning. f) [1.5 points] Say that the mirrors are not exactly parallel but are at a slight angle to each other- as is shown in the diagram. How does this affect what is seen by the person looking into the front mirror? Explain your reasoning. As part of your explanation, remake the diagram (either in another color, or with clear labeling) showing the series of images in these slightly tilted mirrors.