# Download ECE 181 Spring 2017 Homework Assignment 3: Due Tuesday May

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```ECE 181 Spring 2017 Homework Assignment 3:
Due Tuesday May 2
Problem 1: A renaissance-era telescope maker has become extremely good at making one kind of lens, a planoconvex glass singlet that is 10 mm in diameter and has a 40 mm focal length.
(A) Given that this glass has index ng = 1.6, use the lens makers equation 1/f = (ng-1)[(1/R1) - (1/R2)] to
calculate the radius of curvature of the convex side. Sketch the singlet lens to scale, identifying the radius
of curvature and the center thickness of the lens, where the center thickness has been chosen so that the
edge thickness of the lens is nearly zero.
(B) Two of the same plano-convex singlet lenses are now combined to construct an compound objective lens
whose paraxial focal length is 22 mm. Treating the lenses as "thin", what is the physical spacing between
the lenses?
(C) The lenses from (B) are now used in a 1:1 imaging system. Sketch the position of both lenses, object, and
the image, and the parallel, chief, and axial rays.
Problem 2:
Fiber coupling spherical lens. Tiny glass balls are sometimes used as lenses to couple light into and out of single
mode optical fibers, because they are cheap to manufacture. The fiber is located a distance f (the back focal
distance of the ball lens) from the rear surface of the sphere, as shown below.
For a sphere of radius a = 1mm and refractive index n = 1.8, and considering a parallel ray a distance y = 0.7
mm away from the optical axis,
(A) What is the paraxial focal length of this lens?
(B) Determine if this ray can be accurately traced using a paraxial approximation (show your calculation).
(C) Find the back focal distance length f such that this ray at height y = 0.7 will be focused to the center of the
optical fiber.
(D) Find the effective focal length of the ball lens for this specific parallel ray.
Problem 3: Relay imaging
Hint: Show that this causes the stability condition (Eq 1.4-32 in text) to be satisfied.
```