Show that the effective focal length of a sphere of radius R made of a material whose refractive index is n and surrounded by air is f = nR / (2 (n - 1)). Show that the two principal planes coincide and cut the sphere in half.
Added by Carlos N.
Step 1
Step 1: Start with the lens maker's formula: 1/f = (n-1) * (1/R1 - 1/R2), where f is the focal length, n is the refractive index, R1 is the radius of curvature of the first surface, and R2 is the radius of curvature of the second surface. Show more…
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