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

Refraction at a spherical interface: Paraxial ray approximation Snell’s law ____________________________ 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’

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

Definition: Focal points of a curved interface

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

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

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

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

Refraction at a spherical interface In paraxial ray approximation: Imaging occurs according to:

Object-image height relationship

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

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

Thin lenses Treat as two spherical interfaces Assume that the lens thickness t is negligible n n’ O I C2 C1 nL R1 R2 s s’

Thin lens: First surface P’ P V R1 s, R1 > 0 s s” s” < 0 since to the left of V

Thin lens: Second surface P’ t nL s” s’

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

Thin lens First interface Second interface

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

Thin lens (nL=1.5): Examples Double convex lens |R1| = |R2| = 20 cm f =____ P = _____ Double concave lens Plano-convex

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

Thin lens: Ray diagrams

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

Reflection at a curved mirror interface Show that: