Part 1: A thin lens has a crescent shape, which is defined by two spherical surf

Question

Part 1: A thin lens has a crescent shape, which is defined by two spherical surfaces A and B. The radius of the surface A is |RA| = 3a, and of surface B is |RB| = a. The lens is submerged in a medium.

What is the magnitude of the focal length |f | in the small angle approximation? Assume the index of refraction of the lens is 2.0 and of the medium is 1.0.

Part 2: The sign of the focal length is (positive or negative)?

Part 3: What will be the magnitude and the sign of the focal length when the lens is flipped over?

Explanation / Answer

1)
1/f = (n-1)(1/R1 - 1/R2)

1/f = (2-1)*(1/3*a + 1/a)

1/f = 1/a *(1/3 + 1)

1/f = 1/a*(4/3)

==> f = (3/4)*a

2) positive

3)

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