A solar cooker, really a concave mirror pointed at the Sun, focusesthe Sun’s rays 18.0 cm in front of the mirror. What is the radius ofthe spherical surface from which the mirror was made?
Question
A solar cooker, really a concave mirror pointed at the Sun, focusesthe Sun’s rays 18.0 cm in front of the mirror. What is the radius ofthe spherical surface from which the mirror was made?
Solution
The radius of curvature of a mirror is twice the focal length. This is based on the mirror formula which is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance. For a mirror, the object distance is infinity, so the formula simplifies to 1/f = 1/v, which means the focal length is equal to the image distance.
In this case, the solar cooker focuses the Sun's rays 18.0 cm in front of the mirror, so the focal length is 18.0 cm.
Therefore, the radius of the spherical surface from which the mirror was made is 2 * 18.0 cm = 36.0 cm.
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