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Paraxial Ray tracing problem

Paraxial Ray Tracing Problem

Consider a convex lens with the first surface having a radius of curvature of 31.123mm, a lens thickness of 5.8mm, and the second surface of the lens is flat. The lens is made from a glass whose diameter is 30mm.

Assume that an object is held 300mm to the left of the lens that glows at two wavelengths 486.1 nm blue and 656.3nm red. The refractive index of the lens at these two wavelengths is 1.522376 for the blue and 1.514322 for the red. Because the refractive index is not the same for both wavelengths, there will be two images. Find the image distances from the rear surface of the lens for each of these two wavelengths, as well as the focal lengths.

Assume the object is a star and that you focus on the red image. What is the diameter of the blue image as predicted by paraxial ray tracing.

Solution Preview

Please see the attached file.

SOLUTION

Fundamentals in a nutshell

1. Lens maker's formula : 1/f = (n -1)(1/R1 - 1/R2) .........(1)

where : R1 = Radius of curvature of lens surface 1
R2 = Radius of curvature of lens surface 2
n = refractive index of the material of the lens
f = focal length of the lens

Sign convention : In applying the above formula following sign convention is followed :

i) All distances are measured from the optical centre of the lens.

ii) Distances measured in the direction of the incident ray are positive and those in ...

Solution Summary

The expert examines paraxial ray tracing problems. The refractive index of the lens with two wavelengths are determined. Step by step solution provided.

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