Physics 1B03summer-Lecture 11

Interference of LightInterference of Light

Light is an electromagnetic (EM) wave.

Wave properties:

Diffraction – bends around corners, spreads out from narrow slits

Interference – waves from two or more coherent sources

interfere

Physics 1B03summer-Lecture 11

Double SlitDouble Slit

Result: Many bright “fringes” on screen, with dark lines in between.

screen

double slit

separation d

θ

m=2m=1

m=0 (center) m=-1 m=-2

incident light

Physics 1B03summer-Lecture 11

A very thin transparent sheet placed over BOTH slits delays the waves passing through both slits by one-quarter cycle. What happens?

A) The interference fringes disappearB) The fringes all shift upwardsC) The fringes all shift downwardsD) There is no change to the pattern.

Concept Quiz

Physics 1B03summer-Lecture 11

Example

A double slit interference patter is observed on a screen 1.0m behind two slits spaced 0.3mm apart.

Ten bright fringes span a distance of 1.65 cm.

What is the wavelength of light used ?

Physics 1B03summer-Lecture 11

Individual waves (one slit open at a time), I1 = I2 = Io

where Io = (constant) x Eo

2

Both slits open:

sin

22 with

)(cos4 212

0

dr

IIR

Intensity:

sin

cos 2 dIR

Physics 1B03summer-Lecture 11

Notes:

1) Maximum IR is 4 x IO. This is twice as large as the intensity “should” be (in the absence of interference).

2) At the minima, adding the second wave reduces the resultant intensity to zero, instead of doubling it. Averaged over the entire pattern, the total energy does add up to the sum of the energies in the individual beams.

Physics 1B03summer-Lecture 11

Refractive IndexRefractive Index

material refractive index speed of light

vacuum 1 c 300,000 km/sair 1.0003glass about 1.5 200,000 km/swater 1.333 225,000 km/sdiamond 2.4 125,000 km/s

The speed of light depends on the material. We define the refractive index “n” as

n = (speed of light in vacuum)/(speed of light in a material)

Physics 1B03summer-Lecture 11

A beam of yellow light (wavelength 600 nm), travelling in air, passes into a pool of water. By what factor do the following quantities change as the beam goes from air into water?

A) speed B) frequency C) wavelength

Physics 1B03summer-Lecture 11

Reflection and Phase Reflection and Phase ChangeChange

Light waves may have a 180° phase change when they reflect from a boundary:

“optically dense” medium (larger refractive index)

no phase change at this reflection180° phase change

when reflecting from a denser medium

Just remember this : low to high, phase shift of pi !

Physics 1B03summer-Lecture 11

Example: Thin filmExample: Thin film

What is the minimum thickness of a soap film (n 1.33) needed to produce constructive interference for light with a 500nm wavelength ? (air : n 1.00).

What about destructive interference ?

Physics 1B03summer-Lecture 11

Example: Antireflection Example: Antireflection coatingscoatings

To reduce reflections from glass lenses (n 1.5), the glass surfaces are coated with a thin layer of magnesium fluoride (n 1.38). What is the correct thickness of the coating for green light (550 nm vacuum wavelength)?

MgF2air glass