 #1
youmei0426
 18
 0
 Homework Statement:

An achromatic lens is to be made by combining planoconvex and planoconcave lenses made from two different types of glass, A and B. These have the following refractive indexes:
red light: A  1.51 B  1.64
blue light: A  1.53 B  1.68
What radii of curvature should be used to produce a combination equivalent to a converging lens with a focal length of 500mm?
 Relevant Equations:

1/f = 1/f_1 + 1/f_2
1/f = (n1)(1/R_1+1/R_2)
R  curvature
n  refractive index
f  focal length
Since the two lenses are planoconcave and planoconvex, the lens maker equation can be simplified into containing only 1 R for each of the lens. Substituting the values for the red light, I got: 1/f_{1}=0.51/R_{1} and 1/f_{2} = 0.64/R_{2}. Adding these two equations and equating them to 1/(500*10^{3}).
However, this equation clearly has two variables. I'm sure we need to use the data for the blue light, but I am not sure how I can incorporate them into the equations? The curvatures of the lenses should not change as the wavelength changes...
Thanks in advance for the help!
However, this equation clearly has two variables. I'm sure we need to use the data for the blue light, but I am not sure how I can incorporate them into the equations? The curvatures of the lenses should not change as the wavelength changes...
Thanks in advance for the help!