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Optical systems: Magnifier, microscope, telescope & binoculars . Hecht 5.7 Wednesday October 9, 2002. Hand Magnifier. What is the angular magnification of the image for an object at the near point or at ∞?. With thin lens. H,H’. h”. θ ’. F. s o. h M ’. l. f. s’. L.

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optical systems magnifier microscope telescope binoculars

Optical systems:Magnifier, microscope, telescope & binoculars

Hecht 5.7

Wednesday October 9, 2002

hand magnifier
Hand Magnifier

What is the angular magnification of the

image for an object at the near point or at ∞?

With thin lens

H,H’

h”

θ’

F

so

hM’

l

f

s’

L

compound microscope
Compound Microscope

x’

L

Fe

Fo

Fo

Fe

Recall xx’ = fo2

x

x’ ≈ L

Wish to have intermediate image (h’)

just inside the focus of the eyepiece

x = fo2/L

s’ ≈ fo + L

s = x + fo

compound microscope1
Compound Microscope

L

Fe

h

h’

Fo

Fo

Fe

h”

  • Recall: The magnification of an image formed
  • at the near point is
  • at infinity
compound microscope2
Compound microscope

Total magnification

(Image at infinity)

(Image at near point)

compound microscope3
Compound Microscope

In most microscopes, L ~ 16 - 17 cm

Objective

Eyepiece

(image at ∞)

10 X, 20 X, 40 X etc

fe = 2.5 cm

10X 

Me = 10

40X  fo = 0.4 cm

Overall magnification M = 40X10 = 400

compound microscope4
Compound Microscope

L

A.S.

Fe

Fo

Fo

Fe

EnP

ExP

Where should the eye be located to view the image?

  • Optimum viewing –
  • Place eye near ExP (moving eye away decreases illumination and F.O.V.)
  • Ensure that exit pupil ~ same size as eye pupil!
compound microscope5
Compound Microscope

L

A.S.

Fe

Fo

Fo

Fe

EnP

ExP

Chief Ray

Marginal ray

numerical aperture
Numerical Aperture

Measure of light gathering power

N. A. = n sin α

Lens

Air

Oil

αg

αg’

αo

αa

Cover Glass

ng

O

numerical aperture1
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 ng = 1.5

Increases the light gathering power by about 1.5

(N.A. roughly analogous to f# of a lens)

numerical aperture2
Numerical Aperture

In optical fibres

Cladding n2

Core n1

θc

θ

no

αmax

Cladding n2

N.A. = nosinαmax= n1sin θ = n1sin (90o - θc) = n1cos θc

This is a measure of the maximum cone of light accepted

viewing distant objects e g stars
Viewing distant objects, e.g. stars

star

h

θ

feye

Image size on retina h = feyeθ

telescope
Telescope

Objective

Eyepiece

fo

fe

hT=feyeθ’

θ’

θ

h’

θ’

h”

s’

telescope1
Telescope

Show

(magnification of the telescope)

(diameter of the exit pupil)

slide15

The Hubble Space Telescope

0.3 m secondary

mirror

2.4 m primary

mirror

binoculars
Binoculars

Two telescopes side-by-side

Prisms used to erect images

Objective

Eyepiece

binoculars1
Binoculars

“6 X 30”

Angular Magnification (M)

Diameter of objective lens, Do (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