Images and Optical Instruments

Definitions• Real Image - Light passes through the image point.

• Virtual Image - Light does not pass through the image point.

• Magnification– Negative means the image is inverted.

h

h

heightobject

heightimageM

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Plane Mirror

• Plane Mirror Properties s’ = s M = 1 Image is virtual and erect Image has right-left reversal

Mirror Image

s s’

Spherical Mirror• Focal Point - Location where parallel

incoming rays converge or appear to converge.

2

Rf

s

s

h

hM

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fss

1

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11

R R

Concave Mirror Convex Mirror

MagnificationFocal Length Image Distance

Concave Mirror• s, s’, f, and R are positive values

• Image is inverted and real

R

f

s

s’

Convex Mirror• s is positive

• s’, f, and R are negative

• Image is erect and virtual

R

s s’

Grocery Shopping• In a grocery store you see an aisle mirror

which is convex with a 1.0 m radius of curvature. How tall is your image if you are 2.0 m tall and 3.0 m away from the mirror?

Images from Refraction

• Assuming small incidence angle

• Use positive numbers for values when– s in front of the surface (Real Object)– s’ & R in back of the surface

• Use negative numbers for values when– s in back of the surface (Virtual Object)– s’ & R in front of the surface

R

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s

n

s

n 1221

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sn

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Fish and the Kitten

• A kitten is located 10 cm from a fish bowl with a 2.0 m radius of curvature. Where is the image of the kitten and tall is it if the kitten is 20 cm tall.

Thin Lenses• A lens consists of two refracting surfaces.

• For thin lenses

• Positive– s in front of the lens, s’, R1 and R2 behind

• Negative– s in back of the lens, s’, R1, and R2 in front

21

111

'

11

RRn

ss

R2

R1

Thin Lenses• Convex Lens - Converging

• Concave Lens - Divergingfocus

Parallel Light Rays

focus

Parallel Light Rays

s

s

h

hM

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fss

1

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11

Vision ProblemsHyperopia – farsightednessCorrected with a convergent lense.

Myopia – nearsightednessCorrected with a divergent lense.

Diopters = m-1fP 1Lens’ Power

Microscope• Objective and eyepiece separated by a fixed distance, L.

fe

L

fo

Lateral MagnificationM=-s’/s

Angular MagnificationMax M=1+25/fRelaxed M=25/f

Near Point = 25 cm

Telescopes

Refractor Reflector

ef

fm 0

0

f0

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Eyepiece

Objective

Color Vision

• Additive Color Theory– Primary Colors

• Red

• Green

• Blue

– Secondary Colors• Yellow

• Cyan

• Magenta