Problem Set 4: Principal Planes

Problem Set 4: Principal Planes#

You will be designing and analyzing a zoom lens made using perfect lenses. Your zoom lens should have a focus range of \(7 mm \lt f \lt 26 mm\). Read over the design section on Wikipedia.
1. What are the focal lengths of the 4 lenses?
2. Create a plot of the required positions of the two moving lenses as a function of focal length.
(See Problem 4.11) An optical system consists of two thin lenses of focal lengths F1=100mm, F2=25mm, separated by a distance of d=140mm.
1. Calculate the equivalent power of the whole system and the principal planes.
2. Sketch the optical system with lenses and principal planes labeled.
3. Trace several rays through the system using the principal planes for an object located 833.3mm in front of the first lens.
4. Create a plot with 4 different rays traced from the tip of the object (at 833.3mm in front of the first lens). This ray tracing should be done using ABCD matrices.
(Problem 4.14) Two positive thin lenses are separated by a distance of 10cm. The focal lengths are F1=10cm, F2=20cm. Determine the power of the combination and the location of both principal planes.
(Problem 4.23 parts a and b only) A thin lens of F=4cm is followed by another thin lens of F=2cm. The distance between the lenses is 4cm.
1. Determine the location of both principal planes and the total system power.
2. Using the principal planes, determine the image location and magnification for an object located 8cm in front of the first lens.
The prescription of a Cooke Triplet is

Radius

Thickness

Glass

32.25 mm

6 mm

LASFN31

188.25 mm

8.1 mm

-144.5 mm

1.0 mm

SF57

28.72 mm

17.9 mm

139.6 mm

2.5 mm

LASFN31

-88.0 mm

The best method to find the refractive index of the glasses is to use OSLO. The glass can be found in the Schott catalog.
1. Find the effective focal length and principle planes for a Cooke Triplet. Use a wavelength near 488 nm and use the paraxial approximation. Use the thin lens approximation.
2. Use OSLO to calculate the actual effective focal length.
(Problem 5.12) A positive thin lens (F1=10cm) is followed by a negative thin lens (F2=-5cm). The distance between the two lenses is 2cm. The first lens has a diameter of 1.5cm, and the second lens has a diameter of 1cm. For an object at infinity, determine the following: position and size of the entrance and exit pupils, position of the field stop (or nearest equivalent), and the paraxial angle (semifield of view).

Radius	Thickness	Glass
32.25 mm	6 mm	LASFN31
188.25 mm	8.1 mm
-144.5 mm	1.0 mm	SF57
28.72 mm	17.9 mm
139.6 mm	2.5 mm	LASFN31
-88.0 mm