A single concave spherical mirror is used to create an image of a source 7.27 cm
ID: 1978335 • Letter: A
Question
A single concave spherical mirror is used to create an image of a source 7.27 cm tall that is located at position x = 0 cm which is 25.4 cm (= 2l) to the left of Point C, the center of curvature of the mirror, as shown in the figure. The magnitude of the radius of curvature for the mirror is l = 12.7 cm.
a) Calculate the position xi where the image is formed. Use the coordinate system given in the drawing.
b) What is the height hi of the image? Enter a positive result, if the image is upright (pointing up), or a negative result if the image is inverted (pointing down).
Explanation / Answer
a) focal length = 1/2(radius of curvature) = 1/2*l = 1/2(12.7) = 6.35 cm do = distance of object from mirror = 3l = 3(12.7) = 38.1 cm di = distance of image from mirror = ? 1/f = 1/do + 1/di ===> 1/di = 1/f - 1/do = (1/6.35) - (1/38.1) therefore di = 7.62 cm (since it is positive the image is also in front of the mirror) b) you can use the magnification equation to get hi: di/do = hi/ho ==> di*ho = do*hi ==> hi = di*ho/do = 7.62*7.27/38.1 = 1.454 cm if an object is further away from a concave mirror than the center of curvature, the image is always inverted...therefore, the answer is negative = -1.454 cm.
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