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```Midterm exam OPTI 518 Spring 2015
You can use a computer, a calculator, your class summary, and your class notes.
75 minutes.
In answering the questions below write down the pertinent formulas and show how you
use them to do the calculations. Each question is worth 10 points for a total of 100.
Provide labeled graphs and sketches whenever asked.
1) Draw the wavefans for a system having 5 waves of spherical aberration and -10
waves of astigmatism. Draw the sagittal and tangential fans for the zero field
position and the 0.707 field position.
2) Write down the relationship between a change of focus W020 and the longitudinal
change Z ' . For a f/10 system with W020  1 , what is Z ' ? The wavelength is
0.0005 mm.
3) Write down the sag equation to fourth-order for a spherical surface of radius r and
semi-aperture y.
4) A thin, equi-convex, lens in air is made out of BK7 glass, has a focal length of
100 mm and works at F/5. The stop aperture is at the lens and the full field of
view is 48 degrees. Determine the Lagrange invariant, the image height, and the
chromatic aberrations.
5) For the lens in problem 4 what is the amount in waves (1 wave = 0.0005 mm) of
spherical, coma, and astigmatism aberrations?
6) For the lens in problem 4 what is the Petzval radius? What is the amount of
distortion aberration?
7) For the lens in problem 4 design an aspheric surface on a parallel glass plate that
corrects only for spherical aberration. This aspheric plate has zero optical power.
Where should the aspheric plate be located? and what is the sag of the aspheric
profile of the plate? Assume the index of the plate to be n=1.5. Sketch the system.
8) For the system in problem 7 add a field flattener lens to correct for Petzval field
curvature. What is the power of the field flattening lens? Sketch the plate, lens
and field flattener system. Sketch the field curves.
9) A point source of light is at the bottom of a swimming pool which has a depth of
3350 mm. The light is then collected by a lens with an aperture of 2000 mm
located at 5000 mm above the swimming pool. Using an index of refraction for
water of 1.33, determine how much spherical aberration the water-air interface is
introducing.
10) Provide the amount of defocus for minimum wavefront variance, to reach the
minimum circle, and for minimum spot size in the presence of five waves of
positive spherical aberration.
```