Principal planes method For the purposes of finding images, we can reduce any* optical system to a thin lens. Principal plane distances p 1 and p 2 are “added” to the physical system, and distances d o and d i are measured from the planes. (*The system must begin and end in the same index, and paraxial approx).

Principal planes method Imaging equation: Magnification p 1 or p 2 can be negative If these = 1, then is 0.

The effective focal length is ___ cm a)1 b)2 c)3 d)4 e)5 For a thick lens Assume thickness d=2 cm, R ­1 = 2 cm, R 2 =  and n=2

The principal planes are ___ cm from the edges 1 and 2 a)2, 3 b)0, 2 c)0, -1 d)1, 4 For a thick lens Assume thickness d=2 cm, R ­1 = 2 cm, R 2 =  and n=2

Where will parallel laser light (object at infinity) be focused if coming from the left? …if from the right? If an object is 3 cm to the left of the lens edge, find the position of the image vs the right edge.

Two equivalent methods 1.Today’s: Add principal planes to find ABCD effective. Set the diagonal elements to 1 to find p’s. Treat as thin lens, use thin lens imaging equation 2.Last lecture: add d o and d i to find ABCD total Find imaging equation by setting B total = 0.

Laser stability criterion Stability: , y remain small after many round trips

Stable cavities

Laser stability criterion Geometrical interpretation of A cavity is stable if the segments between the mirrors and their centers of curvature partially overlap. (One cannot lie entirely within the other)

Laser stability criterion For mirrors R o and 2R o, the cavity will be stable if L is ____ a)0 …R o b)R o …2R o c)R o …3R o d)2R o …3R o e) two of the above

Laser stability criterion If a diverging mirror (-R o ) is used and a converging one (2R o ) find all allowable L’s a)0 …R o b)R o …2R o c)R o …3R o d)2R o …3R o e) two of the above