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Document info12.

Thick Lenses and the

ABCD Formalism

Thursday, 10/12/2006

Physics 158

Peter Beyersdorf

1 12.

Class Outline

Properties of Thick Lenses

Paraxial Ray Matrices

General Imaging Systems

2 12.

Thick Lenses

3 When the thickness of a lens is not negligible compared to the object and image distances we cannot make the approximations that led to the "thin lens formula", and requires a few additional parameters to describe it

Front and Back focal lengths

Primary and secondary Principle planes

12.

Terms used with Thick Lenses

4 Focal lengths are measured from the vertex of the lens (not the center) and are labeled as the front focal length and the back focal length. An effective focal length is also often used... Principle Planes are the plane approximations to the locust of points where parallel incident rays would intersect converging exiting rays. There is a primary (on the front side) and a secondary (on the back side) principle plane. These are located a distance h 1 and h 2 from the vertices. These distances are positive when the plane is to the right of the vertex. h 2 f(n l -n m )d l R 1 n l 12.

Imaging with a thick lens

5 The same derivation used for the thin lens equation can be used to show that for a thick lens provide the effective focal length given by is used, and the distances s o and s i are measured from the principle points located at 1 s i 1 s o 1 f 1 f =(n l -n m 1 R 1 1 R 2 (n l -n m )d l n l R 1 R 2 s o s i primary principle plane secondary principle plane n l n m d l h 1 f(n l -n m )d l R 2 n l 12.

Thick Lens Parameters

6 s o s i primary principle planesecondary principle plane n l n m d l h 2 f(n l -n m )d l R 2 n l h 1 f(n l -n m )d l R 2 n l 1 f =(n l -n m 1 R 1 1 R 2 (n l -n m )d l n l R 1 R 2 h 1 h 2 note h 1 and h 2 are positive when the principal point is to the right of the vertex 12.

Example

For the lens shown, find the effective focal

length and the principle points (points where the principle planes intersect the optical axis) if it is made of glass of index 1.5 and is in air 7 3mm R 2 =10mmR 1 =12mm Note: Radius of curvature is considered positive if the vertex of the lens surface is to the left of its center of curvature h 1

80mm(1.5-1)3mm

12mm(1.5)

=-6.7mmh 2

80mm(1.5-1)3mm

10mm(1.5)

=-8mm 12.

Example

For the lens shown, find the effective focal

length and the principle points (points where the principle planes intersect the optical axis) if it is made of glass of index 1.5 and is in air 8 3mm R 1 =10mmR 2 =12mm 1 f =(1.5-1) 1 10mm 1 12mm (1.5-1)3mm

1.5(10mm)(12mm)

f=80 mm 12.

Example

Find the focal length and locations of the

principle points for a thin lens system with two thin lenses of focal lengths 200mm and -200mm separated by 100mm 9 f=200 mmf=-200 mm100 mm 12.

Example

Find the focal length and locations of the

principle points for a thin lens system with two thin lenses of focal lengths 200mm and -200mm separated by 100mm 10 f=200 mmf=-200 mm100 mm b.f.l=200 mm h 2 =-200 mm f eff =400mm |h 2 |b.f.l 12.

Example

Find the focal length and locations of the

principle points for a thin lens system with two thin lenses of focal lengths 200mm and -200mm separated by 100mm 11 f=200 mmf=-200 mm100 mm f.f.l=600 mm h 1 =-200 mm f eff =400 mm h 2quotesdbs_dbs11.pdfusesText_17