Lenses mirrors and refractive surfaces Friday Sept 13

Lenses, mirrors and refractive surfaces Friday Sept. 13, 2002

Refraction at a spherical interface: Paraxial ray approximation n Snell’s law ______________ n Leads to… Governs refraction at an interface All rays from O pass through I, i. e. I = image of O For a given object distance s, can find a conjugate distance s’ 2

Definitions: Focal points of a curved interface 1. Focal Points: Governs refraction at an interface Suppose object at s = All rays arriving at lens will travel parallel to optic axis and, This defines the second focal point 3

Definition: Focal points of a curved interface f’ 4

Definitions: Focal points of a curved interface 1. Focal Points: Suppose image at s’ = All rays leaving lens will travel parallel to optic axis and, This defines the first focal point. 5

Focal points for curved interface Show Definition: Focal points, f, f’ are conjugate with s, s’ = 6

Definitions: Power n’>n Power of surface P > 0 for converging surface C n P < 0 for diverging surface R>0 n’ R<0 C n 7 n’

Definitions: Power n Thus if n’ > n and R< 0 f, f’, and P are all negative In general, 8

Refraction at a spherical interface f f’ h h h’ s n R n’ C h’ s’ In paraxial ray approximation: Imaging occurs according to: 9

Object-image height relationship 10

Lateral Magnification Since h is negative True for all imaging according to 11

Lateral magnification f f’ h R s n In above, since s, s’ > 0 C n’ h’ s’ m < 0 inverted image New image shown in figure is q real (light actually passes through) q inverted q demagnified or reduced 12

Thin lenses Treat as two spherical interfaces Assume that the lens thickness t is negligible n n’ O I C 2 C 1 n. L R 1 s R 2 s’ 13

Thin lens: First surface n P’ P n. L V R 1 s, R 1 > 0 s s” 14 s” < 0 since to the left of V

Thin lens: Second surface n n’ R 2 P’ t n. L s” s’ 15

Thin lens: second interface First interface Second interface Object distance t + s” = t - |s”| Thin lens t → 0, so object distance = - |s”| 16

Thin lens First interface Second interface 17

Thin lens In a single medium (n=n’) In air (n = 1) Lens makers formula 18

Thin lens (n. L=1. 5): Examples Double convex lens |R 1| = |R 2| = 20 cm f =____ P = _____ n Double concave lens |R 1| = |R 2| = 20 cm f =____ P = _____ n Plano-convex |R 1| = |R 2| = 20 cm f =____ P = _____ n 19

Thin lens: Power n Thicker in middle P>0 n Thinner in middle P<0 20

Thin lens: Ray diagrams 21

Reflection at a curved mirror interface in paraxial approx. y φ C O ’ I s’ s 22

Reflection at a curved mirror interface Show that: 23