An equiconvex lens of focal lenght 15 cm is cut into two halves of thickness. Find the focal length of each half.
An equiconvex lens of focal lenght 15 cm is cut into two halves of thickness. Find the focal length of each half.
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From the lensmaker's equation, we have a symmetrical lens with R1 = -R2, and because it is a convex lens, R1>0. Then:
1/(15 cm)= (n-1)*(1/R1-1/R2)
1/(15 cm)= (n-1)*(2/R1)
1/(30cm) = (n-1)/R1
The new lenses produced by cutting the original lens in half (and we assume the cut is a flat surface) will have focal lengths:
1/f = (n-1)*(1/R1 + 1/infinity)
1/f = (n-1)*(1/R1 + 0)
1/f = (n-1)/R1
But we already showed that (n-1)/R1 = 1/(30 cm), so the focal length of each half of the lens is 30 cm.
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