Interference of LightInterference of Light

Refraction (a review)Refraction (a review)• Character of the wave Character of the wave

in different in different (transparent) media(transparent) media– wave travels slowerwave travels slower– Index of refraction Index of refraction

n = c/vn = c/v– frequency is constant frequency is constant

(wavelength changes)(wavelength changes)• Law of Refraction Law of Refraction

(Snell’s Law)(Snell’s Law)nn11 sin sin = n = n22 sin sin

Huygens Principle

• Propagation of plane wave by Huygen’s principle

Snell’s Law• Refraction • Similar triangles

2

2

1

1

sinsin

2211 sinsin nn

2

2

1

1

vt

vt

refraction ofIndex

vcn

Young’s Double SlitYoung’s Double Slit

Young’s Double Slit 1801Young’s Double Slit 1801• Conditions for interferenceConditions for interference

sin12 drrL

yL

Ly

tansinLyd

Young’s Double SlitYoung’s Double Slit

Constructive interference phase difference to Constructive interference phase difference to be an integral number of wavelengthsbe an integral number of wavelengths

,......2,1,0 wheresin

mmdL

Lydm sin

Destructive Interference Destructive Interference ConditionCondition

Destructive interference Destructive interference (minima)(minima)

Lyd

2

1m

Lyddm

sin

21

Young’s Double SlitYoung’s Double SlitIntensity behaviorIntensity behavior

tEEtEE

02

01

sinsin

tEtEE 00P sinsin

Young’s Double SlitYoung’s Double SlitIntensity behavior algebraic approachIntensity behavior algebraic approach

tEtEEP sinsin 00

2sin

2cos2 0

tEEP

2

cos2

sin2sinsin BABABA

2cos4

2cos

24

2sin

2cos4

20

220

2220

2

I

E

tEEIavep

Intensity by Phasor Method

180)180(2

2cos4

2cos

24

2

2cos4

2cos2

cos2

20

220

2

220

2

0

0

II

EEI

EE

E

EE

Young’s Double SlitYoung’s Double SlitIntensity behavior averaged over one Intensity behavior averaged over one

periodperiod

sind222II 2

0av

cos

sincos2

0 dIIav

yDdIIav

20 cos

Interference upon ReflectionInterference upon Reflection

• Thin FilmThin Film– in airin air– coatingscoatings

Phase changes upon Phase changes upon ReflectionReflection

Dense to less dense

n1 > n2

Less dense to more dense

n1 < n2

Thin Film in Air (Soap Film)Thin Film in Air (Soap Film)

• Near normalNear normal incidenceincidence

• Conditions for Conditions for reflected light reflected light interferenceinterference

Condition for there to be Condition for there to be constructive interferenceconstructive interference

2

2

)21(

,.....1,0 )21(2

nm

mmL n

Assume

21 nn

Michelson InterferometerMichelson Interferometer

1 22 L L

1 22 L LN