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Optical instrumentOptical instrument光學儀器光學儀器

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Real images Real images 實像實像• Images can be projected on a screenprojected on a screen.

• E.g. What you see on the screen right now is a real image.

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Virtual image Virtual image 虛像虛像• Images can’t be projected on a screen.

• E.g.. Image produced by magnifying glass ( 放大鏡 )

images produced by spectacles for long-sight ( 遠視 )

• Important!!!!Important!!!!

both real and virtual images can be seen by human eyes.

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Rotation of plane mirror through Rotation of plane mirror through

Reflected ray rotate by 2Reflected ray rotate by 2

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Moving the plane mirror though Moving the plane mirror though xx

M2 M1

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Convex lens Convex lens 凸透鏡凸透鏡 ((Converging lens 會聚透透鏡鏡 )

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Images of convex lensImages of convex lens

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Images of convex lensImages of convex lens

• Depending on the position of object, either reareal or virtual imagel or virtual image can be produced.

• Real image inverted 倒立

• Virtual image upright 直立

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Concave lens Concave lens 凹透鏡 凹透鏡 (di(diverging lens verging lens 發散透鏡發散透鏡 ))

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Linear magnification, Linear magnification, mm 線性放大率線性放大率

mm = = h’/ hh’/ h = = v / uv / u

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Visual angle Visual angle 視角視角 , ,

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Angular magnificationAngular magnification 角放大率角放大率 , , MM

ii = Visual angle of the image = Visual angle of the image

oo = Visual angle of the object = Visual angle of the object

o

i

M

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Lens/Mirror formulaLens/Mirror formula成像成像 (( 透鏡透鏡 )) 公式公式

fvu

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Magnifying glass Magnifying glass 放大鏡放大鏡

Just a piece of convex lens Just a piece of convex lens 凸透凸透鏡鏡

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D = 25 cmD = 25 cm

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DD: Least distance of distinct visionLeast distance of distinct vision最小明視距離最小明視距離

• DD = = Least distance of distinct vision,

or the distance of the near point near point ( ( 近點 近點 )) from the eye.

• DD = 25 cm = 25 cm.

• When the image is formed at the near point, a magnifying glass is said to be in normnormal adjustment ( al adjustment ( 正常調校 正常調校 ).).

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• Use of magnifying glassUse of magnifying glass: : 0 < 0 < uu < < f f

• Virtual imageVirtual image is formed is formed

• Enlarged and uprightEnlarged and upright

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Magnification of magnifying glassMagnification of magnifying glass

NORMAL ADJUSTMENTNORMAL ADJUSTMENT 正常調校正常調校 (image at D):(image at D):

tan = h / D (without magnifying glass)

• By , uu = D = Dff / ( D + / ( D + ff ) )

= h / u u = [h ( D + f )] / Df

• Angular magnification M:

M = / = ( D + f ) / f = ( D / f ) + 1

fvu

111

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Image at infinity Image at infinity 無窮遠處無窮遠處 ,

vv = = , , uu = = ff : :(This situation is not the case shown in the figure)

= h / f = h / D

M = M = / / = D / = D / ff

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AL MC 01-16

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AL MC 00-20

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AL MC 99-10

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AL MC 97-18

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Compound microscopeCompound microscope複式顯微鏡複式顯微鏡

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• Objective: short fo 物鏡焦距• Eyepiece: long fe 目鏡焦距 , fo < fe

• Separation of the lenses > fo + fe

• To the objective lens: 2f2foo > u > f > u > foo

• Image formed by objective lens is real (enlarged & inverted).

• The real image 真像 produced by objective lens is the “object 物” for the eyepiece lens

• To the eyepiece lens: ffee > u’ > 0 > u’ > 0

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• An enlarged virtual imageenlarged virtual image is produced by the eyepiece lens at Dat D.( in normal adjustment)

• Eyepiece works as an magnifying glass

• Angular magnification M

M = / = ( h2 / D )/( h / D)

= h2 / h

= ( h2 / h1 ) ( h1 / h )

= mmee mmoo

= (eyepiece linear mag.)

x (objective linear mag.)

= h / D = h2 / D

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Refracting telescopeRefracting telescope折射式望遠鏡折射式望遠鏡

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• The focus focus 焦點 焦點 of the objectiveof the objective and that of the eyepieceeyepiece are at the same pointsame point.

• Separation of the lenses = fo + fe

• fo > fe

• The image of distant objectimage of distant object is formed at the focal plane focal plane 焦平面 焦平面 of the objectiveof the objective. This is the “object”“object” for the eyepiece.eyepiece.

• Then the eyepieceeyepiece form an virtual imagevirtual image at iinfinitynfinity.

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• Without telescope, = h / fo

tan = h / fe

• Angular magnification M

M = / = fo / fe , fo > fe

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Eye ring Eye ring 出射光瞳出射光瞳 : : imagimage of objective P formed by eyepiece Qe of objective P formed by eyepiece Q

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• Eye ringEye ring is the position of the eye, when

using an optical instrument, at which most most light enters the eye.light enters the eye.

• Most stars viewed by astronomical telescopes are fainted. The intensity of the final image is further confined by the aperture of the objective. The best position of the eyebest position of the eye is where the light intensity is the greatestlight intensity is the greatest. (eye ring)

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AL MC 99-11

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Grating spectrometer光柵光譜議

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• For spectral analysis (For spectral analysis ( 光譜分析光譜分析 ))

• Measure angular displacement accuratelMeasure angular displacement accuratelyy

• 3 components:3 components:

collimator collimator 準直管準直管turntable turntable 轉盤轉盤 (with grating(with grating 光柵光柵 ))

telescopetelescope 望遠鏡望遠鏡

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• Collimator: produces a parallel beam of light from the source

• Turntable: with diffraction gratingdiffraction grating,can be rotated, the edge of the table has

a scale in degreescale in degree

• Telescope:can be rotated, measure angle of deviation of light through the grating

[receive parallel beam of light][receive parallel beam of light]

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Adjustment before experimentAdjustment before experiment

• TelescopeTelescope:

ready to receive parallel light.

view a distant object and then adjust the eyepiece until the image is focused at eh cross wire.

• collimatorcollimator:

produces parallel light. (without grating)(without grating)

aligning the telescope with the collimator and then adjusting the position of the slit until the image of the slit is focused at the cross-wire.

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• TurntableTurntable:

adjusted to horizontal

by spirit level and the 3 leveling screws underneath

Lastly, mount the gratingmount the grating on the horizontal turntable.

By turning the telescope, each line of the each line of the spectrum can be located accurately (spectrum can be located accurately (angleangle)).