p35_008 - 8. We apply the law of refraction, assuming all...

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Unformatted text preview: 8. We apply the law of refraction, assuming all angles are in radians: sin sin = n w n air , which in our case reduces to /n w (since both and are small, and n air 1). We refer to our figure, below. The object O is a vertical distance h 1 above the water, and the water surface is a vertical distance h 2 above the mirror. We are looking for a distance d (treated as a positive number) below the mirror where the image I of the object is formed. In the triangle OAB | AB | = h 1 tan h 1 , and in the triangle CBD | BC | = 2 h 2 tan 2 h 2 2 h 2 n w . Finally, in the triangle ACI, we have | AI | = d + h 2 . Therefore, d = | AI | h 2 = | AC | tan h 2 | AB | + | BC | h 2 = h 1 + 2 h 2 n w 1 h 2 = h 1 + 2 h 2 n w h 2 = 250 cm + 2(200 cm) 1 . 33 200 cm = 351 cm . .....................................................................................................................................................................................................
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