A plane mirror and a concave mirror ( f = 8.0 cm) are facing each other and are
ID: 2241312 • Letter: A
Question
A plane mirror and a concave mirror (f = 8.0 cm) are facing each other and are separated by a distance of 20.0 cm. An object is placed 8.0 cm in front of the plane mirror. Consider the light from the object that reflects first from the plane mirror and then from the concave mirror. Using a ray diagram drawn to scale, find the location of the image that this light produces in the concave mirror. (Do this on paper. Your instructor may ask you to turn in this diagram.) Specify the distance of this image relative to the concave mirror (include the sign).
1 cm 2---Select---in front of the concave mirrorin back of the concave mirror
Explanation / Answer
Use a one dimensional coordinate system. Consider the plane mirror as the origin and the concave mirror at + 20.0 cm. The object will be at + 8.0 cm. The image formed by the plane mirror will be at - 8.0 cm. This image is (+ 20.0 cm) - (- 8.0 cm) = + 28.0 cm away from the concave mirror.The image formed by the plane mirror is the object of the concave mirror since light from the object is reflected from the plane mirror to the concave mirror.
Use the curved mirror equation: 1/do + 1/di = 1/f. f (focal length of the concave mirror) should be positive since it is a concave mirror. do (distance of the object from the concave mirror) should be positive since the object of the concave mirror is in front of the concave mirror. So f = + 8.0 cm and do = + 28.0 cm. Solving the curved mirror equation for di (distance of the image from the concave mirror) gives us: di = 1/((1/f)-(1/do)). Substitution and arithmetic gives us: di = 11.19 cm. The image formed by the concave mirror is 11.19 cm in front of the concave mirror.
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