Note: Numerical work and use of computer programs is encouraged.
Problem 1:
Find the effective focal length of two thin lenses with focal lengths f1 and f2 , respectively, when they are separated by a distance d. Show or explain your work.
Problem 2:
The focal length of a thin lens depends on the index of refraction n of the material it is made of. Assume you have two thin lenses made from the same material with focal lengths f1 and f2, respectively, separated by a distance d. Find the distance da for which the first order variation of the effective focal length with n is zero. (Such an arrangement is called a Huygens eyepiece.) Show or explain your work.
Problem 3:
Find the matrix connecting the planes O and I.
Problem 4:
For each of the lens types shown above, select example values for R1, R2, thickness D, and indexes of refraction n1, n' and n2, an show the location of the principal planes and the focal points F and F'. You may modify a given spreadsheet, or write your own program.
Problem 5:
An object is 15 cm to the left of a thin converging lens with f = 10 cm. A concave mirror with R = 16 cm is 20 cm to the right of the lens. Determine the location of the principal planes of the system and the location of the image in the following two situations.
 | The rays pass through the lens only once. |
| The rays pass through the lens again after reflection from the mirror. |
Problem 6:
A transparent sphere has a uniform index of refraction n. The image of a distant object lies on the far surface of the sphere. What is the index of refraction of the sphere?