properties of light

Prepared by:Prepared by:Karen A. AdelanKaren A. Adelan

BSE 3 BSE 3

PROPERTIES OF LIGHTPROPERTIES OF LIGHTInterferenceInterferencePolarizationPolarization

Huygens's PrincipleHuygens's Principle

22

Interference of Water WavesInterference of Water WavesAn An interference patterninterference pattern is set up by is set up by water waves leaving two slits at the water waves leaving two slits at the same instant.same instant.

33

Young’s ExperimentYoung’s ExperimentIn In Young’s experimentYoung’s experiment, light from a monochromatic , light from a monochromatic source falls on two slits, setting up an source falls on two slits, setting up an interference interference patternpattern analogous to that with water waves. analogous to that with water waves.

Light source S1

S2

44

The Superposition PrincipleThe Superposition Principle• The The resultant displacementresultant displacement of two simul- of two simul-

taneous waves (taneous waves (blueblue and and greengreen) is the ) is the algebraic sum of the two displacements.algebraic sum of the two displacements.

The superposition of two coherent light waves The superposition of two coherent light waves results in light and dark fringes on a screen. results in light and dark fringes on a screen.

• The The compositecomposite wave is shown in wave is shown in yellowyellow..

Constructive Constructive InterferenceInterference

Destructive Destructive InterferenceInterference

55

Young’s Interference PatternYoung’s Interference Patterns1

s2

s1

s2

s1

s2

Constructive

Constructive

Bright fringe

Bright fringe

Dark fringe

Destructive

66

Conditions for Bright FringesConditions for Bright FringesBright fringesBright fringes occur when the difference in path occur when the difference in path pp is is an integral multiple of one wave length an integral multiple of one wave length ..

pp11

pp22

pp33

pp44

Path difference

p = 0, , 2, 3, …

Bright fringes: p = n, n = 0, 1, 2, . . .

77

Conditions for Dark FringesConditions for Dark FringesDark fringesDark fringes occur when the difference in path occur when the difference in path pp is an is an odd multiple of one-half of a wave length odd multiple of one-half of a wave length ..

pp11

pp22 2

pp33

pp33

2p n

n n = = oddoddn n = = 1,3,5 …1,3,5 …

Dark fringes: 1, 3, 5, 7, . . .2

p n n

88

Analytical Methods for FringesAnalytical Methods for Fringes

x

y

d sin s1

s2

d

p1

p2

Bright fringes: d sin = n, n = 0, 1, 2, 3, . . .

Dark fringes: d sin = n, n = 1, 3, 5, . . .

p = p1 – p2

p = d sin

Path difference Path difference determines light and determines light and dark pattern.dark pattern.

99

Analytical Methods (Cont.)Analytical Methods (Cont.)

x

y

d sin s1

s2

d

p1

p2

From geometry, we From geometry, we recall that:recall that:

Bright fringes:

, 0, 1, 2, ...dy

n nx

Dark fringes:

, 1, 3, 5...2

dyn n

x

sin tany

x

So that . . .So that . . .

sindy

dx

1010

Interference From Single SlitInterference From Single Slit

Pattern ExaggeratedPattern Exaggerated

When monochromatic light strikes a single slit, diffraction from the When monochromatic light strikes a single slit, diffraction from the edges produces an edges produces an interference patterninterference pattern as illustrated. as illustrated.

Relative intensity

The interference results from the fact that not all paths of light The interference results from the fact that not all paths of light travel the same distance some arrive out of phase.travel the same distance some arrive out of phase.

1111

Single Slit Interference Single Slit Interference PatternPattern

a/2

aa/2

sin2

a

1

2

4

3

5

Each point inside slit Each point inside slit acts as a source. acts as a source.

For rays 1 and 3 and for For rays 1 and 3 and for 2 and 4:2 and 4:

sin2

ap

First dark fringe:First dark fringe:

sin2 2

a sin2 2

a

For every ray there is another ray that differs by this path and For every ray there is another ray that differs by this path and therefore interferes destructively.therefore interferes destructively.

1212

Single Slit Interference Single Slit Interference PatternPattern

a/2

aa/2

sin2

a

1

2

4

3

5

sin2 2

a

First dark fringe:First dark fringe:

sina

sina

OtherOther dark fringesdark fringes occur for occur for integral multiples of this fraction integral multiples of this fraction /a/a..

1313

Example 3:Example 3: Monochromatic light shines on a Monochromatic light shines on a single slit of width single slit of width 0.45 mm0.45 mm. On a screen . On a screen 1.5 m1.5 m

away, the first dark fringe is displaced away, the first dark fringe is displaced 2 mm2 mm from the central maximum. What is the from the central maximum. What is the

wavelength of the light?wavelength of the light?

x = 1.5 m y

a = 0.35 mm

= ?

sina

sina

ysin tan ; ;

x

y ya

x a x

(0.002 m)(0.00045 m)

1.50 m = 600 nm

POLARIZATIONPOLARIZATION

1414

Polarized vs. UnpolarizedPolarized vs. Unpolarized

Unpolarized light:Unpolarized light: light wave which light wave which is vibrating in more than one planeis vibrating in more than one plane

Polarized light:Polarized light: light waves in light waves in which the vibrations occur in a single which the vibrations occur in a single plane. plane.

PolarizationPolarization: The process of : The process of transforming unpolarized light into transforming unpolarized light into polarized light is known aspolarized light is known as

1515

Polarized Light

Polarized LightVibrations lie on one single plane only.

Unpolarized LightSuperposition of many beams, in the same direction of propagation, but each with random polarization.

1616

Representation . . . Representation . . .

Unpolarized Polarized

EE

1717

Representation . . . Representation . . .

Unpolarized Polarized

1818

Polarization of LightPolarization of Light

1919

Selective AbsorptionSelective Absorption

Light

Unpolarized

Horizontal Component being Absorbed

Vertical Component being Transmitted

2020

Polarization by AbsorptionPolarization by AbsorptionPolaroid crystalline materials absorb Polaroid crystalline materials absorb more light in one incident plane than more light in one incident plane than another, so that light progressing another, so that light progressing through the material become more through the material become more and more polarizedand more polarized

2121

Crossed Polariods can Eliminate Crossed Polariods can Eliminate LightLight

Huygens’ Principle Huygens’ Principle The first person to explain how wave theory can also account for the laws of geometric optics was Christian Huygens in 1670.The principle states that:

Every point on a wave-front may be Every point on a wave-front may be considered a source of secondary spherical considered a source of secondary spherical wavelets which spread out in the forward wavelets which spread out in the forward direction at the speed of light. The new wave-direction at the speed of light. The new wave-front is the tangential surface to all of these front is the tangential surface to all of these secondary wavelets.secondary wavelets.

2222

2323

Fig 35-17a, p.1108

Huygens’s PrincipleHuygens’s Principle

All points on a wave front act as new sources for the production of spherical secondary waves All points on a wave front act as new sources for the production of spherical secondary waves

k

2424

Reflection According to HuygensReflection According to Huygens

Side-Side-SideDAA’C ADC1 = 1’

Side-Side-SideDAA’C ADC1 = 1’

Incoming ray Outgoing ray

2525

Huygens’ wave front constructionHuygens’ wave front construction

Given wavefront at t

Allow wavelets to evolve for time Δt

r = c Δt ≈ λ

New wavefrontConstruct the wave front tangent to the wavelets