ECEN 4616/5616
Homework 2
Due Mar 5, 2014
Problem Set #2 ECEN 4616/5616
(Due Mar 7, 2014)
Problem 1)
The figure below represents a ray trace through a surface.
a. Indicate the sign of all labeled quantities.
b. Verify that the sign of the relation 𝑢 = −
ℎ
𝑙
is correct.
n
n’
l’
l
C
u
u’
a
h
i
i’
Problem 2)
A thin lens of 5 cm focal length forms an image of a real object located 15 cm
away. What is the magnification?
Problem 3)
A plano convex lens has a power of +3D (i.e., 3 m-1). The curved face has a
radius = 22.97 cm. What is the index of refraction? Does taking the lens
thickness into account make a difference in this calculation?
Notes:
 A plano-convex lens is a positive lens with one flat side.
 “Diopters” (“D”) is a measure of lens power (used for eyeglasses) which
corresponds to 1/f, where f is in meters. i.e., a -6 diopter eyeglass (like
mine) has a focal length of -1/6 m = -16.67 cm.
pg. 1
ECEN 4616/5616
Homework 2
Due Mar 5, 2014
Problem 4)
A biconvex lens has R1 = 5cm, R2 = -3cm, and n = 1.5
a. What is the power of this lens in the thin-lens approximation?
b. What is the power if the center thickness is 6 mm?
c. Assuming the lens is circular, what is the maximum diameter the lens can
be (assuming a center thickness of 6mm) to maintain an edge thickness of
at least 2mm?
d. Extra Credit: Use Zemax to find the answer to part ‘c’.
Note: Very thin or sharp edges should be avoided in glass, as they will
chip very easily, even from contact with much softer materials (like finger
nails or plastic mounts). This phenomenon is known as “pressure flaking”
and is the mechanism by which arrowheads are made.
Problem 5)
The Air Force has decided to convert an empty hanger into a giant pinhole
camera to record a unique image of the decommissioned air base before it is redeveloped into homes and shopping centers. (Note: This really happened.) The
distance from the hanger door (where the “pinhole” is to be drilled) to the back of
the hanger (where the “film” will be hung) is 50 meters.
a. Assuming the mean wavelength of the image will be 0.5 microns,
calculate the optimum size “pinhole” to place in the door to maximize
the image resolution.
b. Find the F/# of the ‘hanger camera’.
c. Assume the ISO rating of the emulsion used (500 gallons worth) is
200. This means that the proper exposure for a sunny scene is 1/200
second at F/16. Assuming a sunny day, find the time that the pinhole
should remain open to properly expose the emulsion. (hint: use the
camera equation)
d. ECEN 5616 (extra credit for 4616): Assuming that the ‘film’ was 50 m
long by 15 m high, what is the total number of effective ‘pixels’
recorded by the camera? (Use the sum of the ‘geometric’ PSF radius
and the ‘diffraction’ PSF radius as the effective radius.)
e. (Extra Credit): Use the PWS (Plane Wave Spectrum) method of
beam propagation to determine the actual PSF size of the ‘optimum’
sized pinhole camera (e.g., D=1.56√(λf)). Use the radius to the first
minimum of the PSF (there won’t be an actual zero null) as the size.
How does this compare to the size of the pinhole?
f. (Extra, extra Credit): Use the relation between the Fourier Transform
of the PSF and the MTF to calculate the diffraction limit spatial
pg. 2
ECEN 4616/5616
Homework 2
Due Mar 5, 2014
frequency of the pinhole camera for a given focal length.
MTF  Ft PSF  
Problem 6)
Design an achromatic, cemented doublet for a telescope objective. The
wavelength range to design to is the span of the F,d,C spectroscopic lines. The
desired focal length is 250 mm and the diameter is 50 mm.
Do the following steps:
a. Choose two glasses from the Schott catalog which you think may work
well.
b. Calculate the paraxial parameters of the elements.
c. Create a starting solution for Zemax (i.e., add thicknesses, pick a
reasonable value for the curvatures). Show the Zemax plots for MTF,
Chromatic Focal Shift, and Seidel coefficients (graphic) for the starting
solution.
d. Optimize on the lens parameters: curvatures and thicknesses to best
focus an on-axis field containing all three wavelengths. Constrain the lens
thicknesses, if necessary, to keep the design ‘reasonable’. Re-plot the
analysis windows from part c for the optimized design.
e. ECEN 5616 (extra credit for 4616): Using Zemax’s “Glass Substitution”
solve, find the best glasses in the Schott Catalog for this lens. You should
be able to use the previous merit function without modification.
f. (Extra Credit for all): Add a third (cemented) element to the lens and let
Zemax find the glasses to make this an ‘Apochromatic’ lens (e.g., the lens
is corrected at 3 wavelengths, instead of just 2 like the achromat. You will
(probably) have to modify the merit function to succeed.
Problem 7)
Using a geometric ray trace, explain why you can illuminate the real image in the
‘Mirage toy’ with a flashlight, even though there is no object there.
pg. 3
ECEN 4616/5616
Homework 2
Due Mar 5, 2014
pg. 4