the two basic measurements obtained using the spherometer, s and h , but does no

Question

the two basic measurements obtained using the spherometer, s and h, but does not provide enough information to relate them to R. Figure C shows the full spherical surface and uses a radius (vertical red line) to bisect the half-circle, creating a base for two triangles. Pythagoras?s Theorem should be sufficient to establish the result of the following exercise:

How do you prove the following formula by using the diagram above? thank you so much. Really need help

Explanation / Answer

EB = s/2, EC = AC - AE = R - h, BC = R. so EB^2 + EC^2 = BC^2 ==> (s/2)^2 + (R - h)^2 = R^2. Now solve to get R = (s^2 + 4h^2)/8h

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