1 Optical systems: Magnifier, microscope, telescope & binoculars Hecht 5.7 Wednesday October 9, 2002

2 Hand Magnifier With thin lens θ’θ’θ’θ’ f F H,H’ hM’hM’hM’hM’ L s’ h” l sosososo What is the angular magnification of the image for an object at the near point or at ∞?

3 Compound Microscope FoFoFoFo FoFoFoFo FeFeFeFe FeFeFeFe L Wish to have intermediate image (h’) just inside the focus of the eyepiece s’ ≈ f o + L x s = x + f o Recall xx’ = f o 2 x’ x’ ≈ L x = f o 2 /L

4 Recall: The magnification of an image formed (a)at the near point is (b)at infinity Compound Microscope FoFoFoFo FoFoFoFo FeFeFeFe FeFeFeFe L h h’ h”

5 Compound microscope Total magnification (Image at infinity) (Image at near point)

6 Compound Microscope ObjectiveEyepiece 10 X, 20 X, 40 X etc 10X  In most microscopes, L ~ cm 40X  f o = 0.4 cm f e = 2.5 cm Overall magnification M = 40X10 = 400 M e = 10 (image at ∞)

7 Compound Microscope FoFoFoFo FoFoFoFo FeFeFeFe FeFeFeFe L A.S. EnPEnP ExPExP Where should the eye be located to view the image? Optimum viewing – Place eye near E x P (moving eye away decreases illumination and F.O.V.) Place eye near E x P (moving eye away decreases illumination and F.O.V.) Ensure that exit pupil ~ same size as eye pupil! Ensure that exit pupil ~ same size as eye pupil!

8 Compound Microscope FoFoFoFo FoFoFoFo FeFeFeFe FeFeFeFe L A.S. EnPEnP ExPExP Chief Ray Marginal ray

9 Numerical Aperture Measure of light gathering power Cover Glass αgαgαgαg αaαaαaαa Air Oil αg’αg’αg’αg’ αoαoαoαo ngngngng N. A. = n sin α Lens O

10 Numerical Aperture If cover glass in air If cover glass immersed in oil (no = 1.516) – between glass and oil there is essentially no refraction since n g = 1.5 Increases the light gathering power by about 1.5 (N.A. roughly analogous to f# of a lens)

11 Numerical Aperture Core n 1 Cladding n 2 In optical fibres nononono α max θ θcθcθcθc N.A. = n o sinα max = n 1 sin θ = n 1 sin (90 o - θ c ) = n 1 cos θ c This is a measure of the maximum cone of light accepted

12 Viewing distant objects, e.g. stars f eye θ Image size on retina h = f eye θ star h

13 Telescope h T =f eye θ’ fofofofo fefefefe ObjectiveEyepiece s’ h” h’ θ’θ’θ’θ’ θ’θ’θ’θ’ θ

14 Telescope Show (magnification of the telescope) (diameter of the exit pupil)

15 The Hubble Space Telescope 2.4 m primary mirror 0.3 m secondary mirror

16 Binoculars Two telescopes side-by-side Prisms used to erect images Eyepiece Objective

17 Binoculars “6 X 30” Angular Magnification (M) Diameter of objective lens, D o (mm) Exit pupil = 5 mm, a good match to the normal pupil diameter For night viewing, a rating of 7 X 50 is better: i.e. ~ 7 mm