The index of refraction of a glass varies with the wavelength of the light passi

Question

The index of refraction of a glass varies with the wavelength of the light passing through it. This has important consequences for the design of optical instruments. A type of glass known as "extra-dense flint" has an n = 1.7378 for blue light, and an n of 1.7130 for red light. Calculate the focal length of the lens above, for both red and blue light.

You will find that red and blue light form images at slightly different distances from the lens. This results in a blurred image. The problem is solved by using systems of lenses composed of glasses having different indices of refraction, and different radii of curvature. Such systems are called either achromatic or apochromatic, depending upon the degree of correction. Designing such a system is a non-trivial exercise, and is beyond the scope of this course.

Explanation / Answer

for blue light 1/f =(µ-1)/R =(1.7378-1)/R =0.7378/R f=R/0.7378=1.355R for red light 1/f =(µ-1)/R =(1.7130-1)/R =0.7130/R f=R/0.7130 =1.4 R

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