GR0877 Problem 15
PROBLEM STATEMENT: This problem is still being typed.
SOLUTION: (E) Recall the lens-maker’s formula: . Here is the radius of curvature of the lens’ surface closest to the light source and is the radius of curvature of the lens’ surface farthest from the light source. Sign convention: the radius of curvature is positive if the center of curvature lies to the right from the lens and is negative otherwise. Let the source of light be situated to the left from each of the lenses. Then for (A) one has , , and . For (B): , . (C): , . For (D) and (E): , , . But , therefore . Alternatively, lenses (A) and (B) are obviously diverging and from (C), (D), (E) the shortest positive focal length has the one that has the smallest radius of curvature, because it bends a set of parallel rays more than the others, hence, the focal point of this lens is the closest to the lens.
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