Physics Assignment

Physics Assignment - Phys 122 TUTORIAL 9 and 10 Reflection...

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Phys 122 Introductory Physics II TUTORIAL 9 and 10 Optics – Reflection and refraction KEY. Reflection. 1. Two plane mirrors are separated by 120°, as the drawing illustrates. If a ray strikes mirror M 1 at a 65° angle of incidence, at what angle θ€ does it leave mirror M 2 ? γ φ 65° 120° α β θ M 2 M 1 SOLUTION From the law of reflection, we know that φ = 65 ° . We see from the figure that φ + α = 90 ° , or α = 90 ° φ = 90 ° – 65 ° = 25 ° . From the figure and the fact that the sum of the interior angles in any triangle is 180°, we have α + β + 120 ° = 180 ° . Solving for β , we find that β = 180 ° – (120 ° + 25 ° ) = 35 ° . Therefore, since β + γ = 90 ° , we find that the angle γ is given by γ = 90 ° β = 90 ° – 35 ° = 55 ° . Since γ is the angle of incidence of the ray on mirror M 2 , we know from the law of reflection that θ = 55 ° . ______________________________________________________________________________ 2. You are trying to photograph a bird sitting on a tree branch, but a tall hedge is blocking your view. However, as the drawing shows, a plane mirror reflects light from the bird into your camera. For what distance must you set the focus of the camera lens in order to snap a sharp picture of the bird’s image? The drawing shows the image of the bird in the plane mirror, as seen by the camera. Note that the image is as far behind the mirror as the bird is in front of it. We can find the distance d between the camera and the image by noting that this distance is the 1 3.7 m 4.3 m 2.1 m Bird Hedge 2.1 m 4.3 m Image

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hypotenuse of a right triangle. The base of the triangle has a length of 3.7 m + 2.1 m and the height of the triangle is 4.3 m. SOLUTION The distance d from the camera to the image of the bird can be obtained by using the Pythagorean theorem: ( 29 ( 29 2 2 3.7 m + 2.1 m 4.3 m 7.2 m d = + = 3. The drawing shows a top view of a square room. One wall is missing, and the other three are each mirrors. From point P in the center of the open side, a laser is fired, with the intent of hitting a small target located at the center of one wall. Identify six directions in which the laser can be fired and score a hit, assuming that the light does not strike any mirror more than once. Draw the rays to confirm your choices. Denote the walls as side A (opposite the target), side B (opposite the open side), and side C (where the target is). The directions in the which the laser will be fired will be the angles measured counterclockwise with respect to the +x axis (i.e., the line from P to the bottom of wall C). We have θ 1 = 11.3 ° , follows a path from C to A to the target. 2 31.0 θ = , follows a path from C to A to B to the target. 3 45.0 θ = , follows a path directly to the target. 4 71 6 θ = . , follows a path from B to the target. 5 135 θ = , follows a path from A to B to the target. 6 162 θ = , follows a path from A to the target. 4. An object is placed in front of a convex mirror. Draw a convex mirror (radius of curvature = 15 cm) to scale, and place an object 25 cm in front of it. Make the object height 4 cm. Using a ray diagram, locate the image and measure its height. Now move the object closer to the mirror, so the object distance is 5 cm. Again, locate its image using a ray diagram. As the object moves closer to the mirror, (a) does the
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