1 Optical systems: The eye, magnifier, microscope, telescope & binoculars Hecht 5.7 Monday October 7, 2002

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3 Human Eye, Relaxed 3.6 mm 7.2 mm 20 mm n’ = mm F F’ HH’ P = 66.7 D

4 Accommodation Refers to changes undergone by lens to enable imaging of closer objects Power of lens must increase There is a limit to such accommodation however and objects inside one’s “near point” cannot be imaged clearly Near point of normal eye = 25 cm Fully accommodated eye P = 70.7 for s = 25 cm, s’ = 2 cm

5 Myopia: Near Sightedness Eyeball too large ( or power of lens too large)

6 Myopia – Near Sightedness Far point of the eye is much less than ∞, e.g. l f Must move object closer to eye to obtain a clear image Myopic F.P. F.P. Normal N.P. MyopicN.P.

7 Myopia e.g. l f = 2m = 67.2 D is relaxed power of eye – too large! To move far point to ∞, must decrease power to 66.7 Use negative lens with P = -0.5 D How will the near point be affected?

8 Laser Eye surgery Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeball Usually use the 10.6 µm line of a CO 2 laser for almost 100% absorption by the corneal tissue Front view Blurredvision

9 Laser Eye surgery Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeball Usually use the 10.6 µm line of a CO 2 laser for almost 100% absorption by the corneal tissue Front view Flattening Distinctvision

10 Hyperopia – Far Sightedness Eyeball too small – or lens of eye can’t fully accommodate Image of close objects formed behind retina

11 Hyperopia – Far Sightedness Suppose near point = 1m Recall that for a near point of 25 cm, we need 70.7D Use a positive lens with 3 D power to correct this person’s vision (e.g. to enable them to read) Usually means they can no longer see distant objects - Need bifocals

12 Correction lenses for myopia and hyperopia

13 Hand magnifier Observation with unaided eye θ

14 Magnifier To maximize the image, bring object as close to the eye as possible, i.e. bring object to near point s = l n = 25 cm θ max h’

15 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 ∞?

16 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

17 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”

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

19 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 ∞)

20 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!

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

22 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

23 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)

24 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

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

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

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

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

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

30 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