Chapter 4's cemented achromatic doublet used crown glass N-BK7

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Wave propagation and light in media

What an Instrument Can See, Ch The optical constants of a medium

Problem

Chapter 4's cemented achromatic doublet used crown glass N-BK7, whose Sellmeier fit gives

n_F = 1.52238

n_d = 1.51680

n_C = 1.51432

at the F, d and C lines (486.13 nm, 587.56 nm, 656.27 nm), hence Abbe number

V_1 = 64.17

. A new doublet is to be built pairing that crown element with a flint glass, N-F2, whose Sellmeier coefficients are

B_1 = 1.34533

B_2 = 0.20907

B_3 = 0.93736

C_1 = 0.0099774\,\mu\mathrm{m}^2

C_2 = 0.0470451\,\mu\mathrm{m}^2

C_3 = 111.8868\,\mu\mathrm{m}^2

, in the Sellmeier form

n^2 = 1 + \sum_i B_i\lambda^2/(\lambda^2 - C_i)

with

\lambda

in micrometres. ((a)) Compute

n_F

n_d

and

n_C

for N-F2, and hence its Abbe number

V_2

. ((b)) The doublet is required to have a total effective focal length of 200 mm and to be achromatic (zero net power change from F to C), so that

\phi_1/V_1 + \phi_2/V_2 = 0

and

\phi_1 + \phi_2 = \phi

. Find the focal length of each element.