Physics 116 Lecture 20 Optical Instruments Nov 1, 2011 R. J. Wilkes - - PowerPoint PPT Presentation

• R. J. Wilkes

Email: ph116@u.washington.edu

Physics 116

Lecture 20

Optical Instruments

Nov 1, 2011

2

Today

Lecture Schedule

(up to exam 2)

• Physics Study Center now staffed by TAs an hour later on

M-W: 9:30 am to 6:30 pm M-W, 9:30am-5:30pm Th, 10:30am-5:30pm F.

• Exam 2 next Monday: same procedures as last time
• Practice exam posted Thursday, in class Friday
• YOU bring bubble sheet, pencil, calculator

Announcements

4

Optical instruments

• We can put together systems of lenses, mirrors, prisms,

polarizers, filters, beam splitters, and all the other optical components we have discussed, to make a variety of common

• ptical instruments, using ray-tracing methods:

– Magnifiers – Microsopes – Refracting telescopes – Reflecting telescopes – Cameras – Projectors

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Telescopes

• Telescopes do 2 things:

– collect a lot of light across a big aperture (opening) and cram this light into your eye

• Lets you see faint objects

– magnify angles by ratio of the focal lengths

• f the main lens/mirror and eyepiece:

Magnification=F/f

• So object looks bigger to you
• Simple operation

– Objective lens forms real image of object inside telescope tube – Eye lens is used as magnifier to view real image made by objective

• Come in two basic varieties:

– refractors, dating back to Galileo’s time (objective = lens)

• Galilean telescope: negative eyelens

– Reflectors (mirror), invented by Newton! – all big telescopes now are reflectors

• Only one surface to grind and polish
• Easier to make in large sizes

Newtonian Reflector Refractor

• Refracting telescopes come in 2 basic varieties
• Inverting (astronomical)
• Objective and eyepiece are both positive lenses
• Image is inverted and viewed at infinity
• That means: parallel rays come out as parallel rays, the

magnification is angular, not linear

• Galilean / non-inverting / “opera glass”
• Objective is positive and eyepiece is negative
• Image is erect and viewed at infinity
• In both cases, the objective makes a real image at the eyepiece focal point

6 F’O FE y F’O FE y

Telescopes

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Telescopes

Gran Telescopio Canarias, 410” reflector, Canary Islands (2009) Yerkes refractor, 40”, Wisconsin (1897) refractor reflector Galilean

Photos: Edmunds Scientific, REI, Wikipedia

Angular vs linear magnification

• Linear magnification is
• Angular magnification is
• Telescopic systems, designed for viewing objects at do = infinity, take

parallel rays in and send parallel rays out – what counts is the angular magnification since no real image is formed.

image

• bject

'

• Angular size of Sun = degree of arc = angular size of Moon

(this coincidence makes total solar eclipses possible!)

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FO

• bject

FE Real, inverted image from

• bjective lens

Objective lens, focal length Fo Eye lens, focal length FE (magnifier) Virtual image formed by eye lens Your eye is part of the

• ptical

system ! cornea/lens retina

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• +x

image

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Lens plane f ’ 2 3 1

• l

l ’

f

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image

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f 3 2 1 Object distance dO Image distance dI

Focal pt

do greater than f Example: camera, or projector

• Focal pt

Rays from object tip re-converge at a point, forming a real, inverted, magnified image (dI is positive) f

• image
• bject

f 2 1

• Object distance dO

Image distance dI

Focal pt

do less than f Example: Magnifying glass

• Focal pt

Rays appear to emerge from a virtual, erect, magnified image, lens equation gives negative dI f

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image

• bject

f 2 1 Object distance dO Image distance dI

Focal pt

do greater than f Example: eyeglasses for myopia

• Gazing through the lens toward

the object, we see rays appearing to emerge from a virtual, erect, demagnified image that is closer than the object, lens equation gives negative dI

do less than f

Very little difference – image just moves a bit closer to the lens

Lens aberrations

• Perfection is impossible!
• Any real lens will not focus all rays reaching its surface onto the

same focal point

• Lens Aberrations:

– Color – different focal points for different wavelengths – Spherical aberration – rays arriving at different distances from the lens axis have different focal points – Coma, astigmatism, curvature of field … many more – quantitative material on aberrations is “cultural” - not on test!

• You should understand qualitative descriptions of aberrations

Not On Test!

Chromatic aberration (CA)

• Simple lenses make images with ‘rainbows’ around objects in white light
• Focal length of lens is different for red, yellow, and blue
• Index of refraction n=n(!)

– For most materials, n decreases with increasing !

• so nBLUE > nYELLOW > nRED
• we get different focal points for different colors:

FB FY FR FR - FB = ACA (Axial Chromatic Aberration) BK1 F2

Typical optical glass n vs l curve: CA is positive for converging lenses, and negative for diverging. We can make a doublet with CA=0 by gluing a negative and positive lens of different n together

Not On Test!

Spherical aberration (SA)

• “Paraxial” ray = ray arriving at lens very close to its optic axis

– Paraxial ray crosses axis at paraxial focus PF (the ordinary “focal point”)

• Marginal ray = ray arriving at lens far from its optic axis

– Marginal rays parallel to axis cross the axis at marginal focus MF

• The difference is called spherical aberration:
• Any refracting surface with spherical shape will have SA

marginal ray paraxial ray MF PF

"M "P

• Envelope of ray paths is the Caustic Surface

– Neck of caustic = Circle of Least Confusion position at which image of a distant pinhole is smallest

caustic surface PF MF x Narrowest point

Not On Test!

17

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Not On Test!

If only vertical, or only horizontal spokes appear sharp, you may have astigmatism