A crown element of N-BK7 is available with and Abbe number (from its Sellmeier fit)

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

A crown element of N-BK7 is available with

n_d = 1.51680

and Abbe number

V_1 = 64.17

(from its Sellmeier fit). It is to be cemented to a dense flint element of N-SF10, whose Sellmeier coefficients are

B_1 = 1.62154

B_2 = 0.25629

B_3 = 1.64448

C_1 = 0.0122241\,\mu\mathrm{m}^2

C_2 = 0.0595737\,\mu\mathrm{m}^2

C_3 = 147.4688\,\mu\mathrm{m}^2

, in the 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-SF10 at 486.13 nm, 587.56 nm and 656.27 nm, and hence its Abbe number

V_2

. ((b)) The doublet must be achromatic with a total effective focal length of 500 mm. Using

\phi_1/V_1+\phi_2/V_2=0

and

\phi_1+\phi_2=\phi

, find the focal length of each element.