1. A square loop of wire with sides of length L = 0.17 m and total resistance R = 50 ohms is moving with constant velocity v into a region of constant magnetic field B = 0.76 T. The magnetic field is perpendicular to the plane of the loop and into the page as shown in the sketch. An induced current of I = 0.043 amperes is flowing around the loop.
[5 points] (a) Which way will the induced current flow in the loop?
[12 points] (b) What is the induced emf that is generated in the loop and causes the current I to flow?
[8 points] (c) What is the value of the constant velocity v of the loop?
2. This problem deals with light passing through a succession of polarizers as indicated in the sketch:
[5 points] (a) Unpolarized light, with an intensity of 1000 W/m2 is incident on the first polarizer. What is the intensity of the light transmitted by the first polarizer?
[7 points] (b) The light now passes through a second polarizer, which has its transmission axis rotated by 30 degrees relative to the axis of the first polarizer. What is the intensity of the light transmitted by the second polarizer?
[8 points] (c) The light transmitted by the second polarizer now encounters a third polarizer, which has its transmission axis oriented at 90 degrees relative to the first polarizer. What is the intensity of the light transmitted by the third polarizer?
[5 points] (d) Suppose the second polarizer is removed. What is the intensity of light transmitted by the two (i.e., first and third) polarizers now?
[5 points] (a) An object is placed 20 cm from a concave mirror, forming a real image. The image position is marked, and the object is now moved and placed there. Where will the image be now? Briefly explain your reasoning.
[8 points] (b) An object is placed 12 cm from a convex mirror with a focal length of -15 cm. On the diagram, sketch the ray diagram showing the position of the image.
[6 points] (c) Where is the image located?
[4 points] (d) What are the image characteristics? (Is the image real or virtual? Upright or inverted?)
[2 points] (e) If the image is 4 cm tall, how tall is the object?
4. A light wave in air has a frequency of 6.0 x 1014 Hz.
[3 points] (a) What is its wavelength?
[3 points] (b) The light wave now enters a block of glass, with refractive index n = 1.5. What is the frequency of the light wave now?
[3 points] (c) What is the wavelength of the light wave in glass?
[7 points](d) The light ray is now incident on a glass-air interface, with an angle of incidence in the glass of 45 degrees. Does the light ray emerge from the glass into air? Explain your answer.
[9 points](e) The far side of the glass block is immersed in water, with a refractive index of 1.33. The light ray is again incident on the interface between glass and water, with an angle of incidence in the glass of 45 degrees. Does the light ray now emerge from the glass block into the water? If so, what is the angle of the refracted ray from the normal to the water-glass interface?
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