Characteristics of the ideal lens –All rays leaving a point on object meet at one point on image –Only one perfect object distance for selected image distance (limited depth of field -- better for smaller lens)
6) Thin lenses a) Converging - thicker in the middle
(i) Parallel coaxial rays converge at focus Reversible
(ii) Symmetric - rays leaving focal point emerge parallel (f’ = f)
b) Sign Convention (left to right) (i)Focal Length: f > 0 converging f < 0 diverging (ii) Object distance d o > 0 left of lens (real; same side as incident light) d o < 0 right of lens (virtual; opposite incident light) (iii) Image distance d i > 0 right of lens (real; opposite incident light) d i < 0 left of lens (virtual; same side as incident light) (iv) Image size h i > 0 erect h i < 0 inverted
c) Lateral magnification Definition: From geometry (and sign convention):
9) Compound Lenses Image of first lens is object for the second lens. Apply thin lens equation in sequentially.
Example: Problem 26.66 Find final image and magnification.
10) Vision and corrective lenses a) Anatomy of the eye
120 x 10 6 rods - detect intensity: slow, mono, sensitive 6 x 10 6 cones - detect frequency: R - 610 nm, G - 560 nm, B - 430 nm
b) Optics - Accomodation: focal length changes with object distance - near point: nearest point that can be accomodated - normally < 25 cm - far point: furthest point that can be accomodated - normally ∞
c) Myopia - far point < ∞ - near-sighted (far-blind) - correction: object at ∞ --> image at far point
Correction: object at ∞ --> image at far point (ignoring the eye-lens distance)
d) Refractive Power For a far point of 50 cm, f = -50 cm, Lens prescription: -2
e) hyperopia (hypermetropia) - near point > 25 cm - far-sighted (near-blind) - correction: object at 25 cm --> image at near point
Correction: object at 25 cm --> image at near point (ignoring the eye-lens distance) For near point of 40 cm, f = 66 cm Power = + 1.5 (reading glasses)
Examples: Problem 26.73 Age 40: f = 65.0 cm --> NP’ = 25.0cm Age 45: NP’ --> 29.0 cm (a) How much has NP (without glasses) changed? (b) What new f is needed? Problem 26.75 FP = 6.0 m corrected by contact lenses. (Find f) An object (h = 2.0 m) is d = 18.0 m away. (a)Find image distance with lenses. (b)Find image height with lenses.
12) Magnifier With magnifier: (Magnifier allows object to be close to the eye)
Without magnifier: Highest magnification (d i = -N): Lowest magnification (d i = -∞): (tense eye) (relaxed eye) (Magnification quoted with N = 25 cm, for relaxed eye)
Example: Problem 26.82 Farsighted person has corrective lenses with f = 45.4 cm. Maximum magnification of a magnifier is 7.50 (normal vision). What is the maximum magnification of the magnifier for the farsighted person without lenses?
13) Compound Microscope Simple magnifier: M = N/f –to increase M, decrease f –practical limits to decreasing f (and therefore size): small lens difficult to manufacture and use increases aberrations Microscope introduces an additional lens to form a larger intermediate image, which can be viewed with a magnifier
L Magnification: For image at ∞, d i2 = f e For max M, d o1 f o For d i2 = ∞, d i1 + f e = L
Example: Problem 26.88 Microscope with f o = 3.50 cm, f e = 6.50 cm, and L = 26.0 cm. (a) Find M for N = 35.0 cm. (b) Find d o1 (if first image at F e ) (c) Find lateral magnification of the objective.
14) The Astronomical Telescope Magnifier requires d o ∞ for stars Introduce objective to form nearby image, then use magnifier on the image
Example: Problem 26.94 Yerkes Observatory: f o = 19.4 m, f e = 10.0 cm. (a) Find angular magnification. (b) If h o = 1500 m (crater), find h i, given d o = 3.77 x 10 8 m (c) How close does the crater appear to be.