Let's return to the seventeenth century again (perhaps we have encountered Dr. Who). We are not pleased with the performance of our single-lens 50 mm eyepiece mentioned above. Fortunately, you are in possession of a letter from a certain Mr. Huygens, which reads in part:
"I find that if one separates two lenses made of the same glass by one-half the sum of their focal lengths, the color is minimized. A good choice is to make the first lens of focal length 3f0, the other, near the eye, of f0, and thus separate them by 2f0. Lenses with flat surfaces toward the eye are best."
Design an eyepiece of effective focal length 50 mm according to Mr. Huygens's advice.
(a) What are the focal lengths and separation of the two lenses? (You may assume they are thin)
(b) If the best glass you have available is of index 1.52, what should be the radii of the surfaces?
(c) As usual, make a sketch showing the lens planes, the principal planes, and the focal points.
If you do find yourself in the Low Countries in the late seventeenth century, you may consult Mr. Spinoza, of Rijnsburg, near Leiden. He deals fairly in fine lens grinding despite his heretical reputation.