Physics 203/204 4: Geometric Optics Images formed by refraction Lens Makers Equation Thin lenses Combination of thin lenses Aberration Optical Instruments

Images formed by Refraction 11 22 for  1 and  2 small(paraxial rays) n 1 s  n 2 s  n 2  n 1 R s s’s’ R

For plane surfaces n 1 s  n 2 s  s=- n 2 n 1 s(virtual image) n 2 n 1  relative index of refraction Thin Lenses Image formed by one refracting surface is Object of second surface

s1s1 s’1s’1 s2s2 I1I1 I2I2 medium 1 medium 2 assume n 1  1 and use the preceding equation 1 s 1  1 s 2  n-1  1 R 1  1 R 2        1 s  1 s for thin lenses s’2s’2

The focal length of a lens is defined as the image distance S'S' when the object is at , i.e. f=s when s= .  1 f  1 s  1 s  n-1  1 R 1  1 R 2       Lens Maker Equation A thin lens has 2 focal points depending on whether incident rays come from left or right. Lateral magnification= m= h h  s s

Lenses Double Convex Plano Convex Convex meniscus

Double Concave Plano Concave Meniscus

Focal length is positive for converging lenses and negative for diverging lenses. Object distance is positive if it is on side of lens that light is coming from (not always true!) Image distance is positive if it is on the opposite side of lens that light is coming from. Object and image heights are positive above the axis, negative below.

o F I 1 2 Ray 1 (appears to) come from focal point Ray 2 passes through center of lens

Combination of thin lenses 1 s  1 s  1 f 1  1 f 2 s=object distance from first lens s=image distance from second lens if the lenses are touching they act as a single lens with focal length 1 f = 1 f 1  1 f 2

Lens Aberrations Lens and mirror equations assume ray makes small angle with optic axis, if this is not the case, imperfect blurred images are formed, this is called ABERRATIONS spherical aberration

chromatic aberration Other Aberrations Astigmatism point object off the axis produces two line images at different points. Coma off axis object produces a coma shaped image Distortion magnification for off axis points different than for on axis points

Optical Instruments Camera The light intensity I incident on the film per unit area is inversely proportional to the square of the ratio of the diameterof the lens to its focal length. The f- number equals the ratio of the focal length to the lens diameter Eye The power of a lens in Diopters is the reciprocal of the focal length measured in meters (including sign)

Simple Magnifier When an object is at the near point of the eye ( 25 cm) the angle subtended by the object is  When a convex lens of focal length f is placed between the eye and the object an image which subtends an angle  0 can be formed at the near point

Compound Microscope objective focal length of f 0 eye piece of focal length f e the two lenses are separated by a distance L For object located just beyond focal point of objective, the two lenses combined form an enlarged virtual and inverted image of lateral magnification M

Astronomical telescope Two convex lenses are separated by a distance equal to the sum of their focal lengths. The angular magnification is equal to the ratio of the two focal lengths