ECE 181 Spring 2013 Homework Assignment 3: Due Tuesday April

ECE 181 Spring 2013 Homework Assignment 3:
Due Tuesday April 28th
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 his 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, assuming 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:
Hint: Show that this causes the stability condition (Eq 1.4-32 in text) to be satisfied.
Problem 3:
Problem 4:
Fiber coupling spherical lens: Tiny glass balls are sometimes used as lenses to couple light into and out of
single mode optical fibers, beacuse they are cheap to manufacture. The fiber is is located a distance f (the back
focal length 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) Determine whether this ray can be accurately traced using a paraxial approximation (show your calculation)
(B) Find the length f such that this ray at height y = 0.7 will be focused to the center of the optical fiber.
(C) Fnd the effective focal length of the ball lens for this parallel ray.