Physics 202 - Galileogalileo.phys.virginia.edu/~pqh/202_17n.pdfPhysics 202 – p. 20/26 Interference...

$: Physics 202 - Galileogalileo.phys.virginia.edu/~pqh/202_17n.pdfPhysics 202 – p. 20/26 Interference and Diffraction Reﬂection of an interface: Air Wedge example A very ﬁne wire$
Physics 202Professor P. Q. Hung

311B, Physics Building

Physics 202 – p. 1/26

Interference and Diffraction

Interference

Light is electromagnetic waves. Shine twolight beams on a given spot and observe thesuperposition of these two beams.

Superposition of two waves can lead toconstructive interference or destructiveinterference.

Physics 202 – p. 2/26


Interference

Physics 202 – p. 3/26


Interference

Physics 202 – p. 4/26


Interference

Constructive interference:Start with two identical sources in phase, i.e.oscillating in the same way. If they continue tooscillate in phase when they reach a givenpoint, the interference is constructive ⇒

Brightest or most intense spot. The conditionfor this to be so is that their difference in pathlengths should be a integral multiple of thewavelength.l2 − l1 = mλm = 0,±1,±2, ...

Physics 202 – p. 5/26


Interference

Destructive interference: Start with twoidentical sources in phase, i.e. oscillating inthe same way. If they are out of phase(crest-to-trough) when they reach a givenpoint, the interference is destructive ⇒ Darkspot. The condition for this to be so is thattheir difference in path lengths should be ahalf-integral multiple of the wavelength.l2 − l1 = (m −

12)λ

m = 0,±1,±2, ...

Physics 202 – p. 6/26


Young’s double-slit experimentYoung’s experiment demonstrated the wavenature of light by showing that two coherent lightbeams can interfere with each other.

Physics 202 – p. 7/26


Young’s double-slit experiment

If light were just “corpuscules”, the screenwould be illuminated just behind these twoslits.

Observation: Light is spread throughout thescreen with bright and dark fringes. ⇒ Wavenature of light.

Physics 202 – p. 8/26


Young’s double-slit experimentHuygens’s principle

Physics 202 – p. 9/26


Young’s double-slit experimentPath Difference

Physics 202 – p. 10/26



Bright Fringes:∆l = d sin θ = mλm = 0,±1,±2, ...

Dark Fringes:∆l = d sin θ = (m −

12)λ

m = 0,±1,±2, ...

Physics 202 – p. 11/26



Physics 202 – p. 12/26


Young’s double-slit experiment: ExampleRed light is used in a double-slit experiment withthe slits separated by a distanced = 1.20 × 10−4 m. Here λ = 664 nm in vacuum.The screen is located at a distance L = 2.75 mfrom the slits. Find the distance y on the screenbetween the central bright fringe and thethird-order bright fringe.

Physics 202 – p. 13/26


Young’s double-slit experiment: Example

The angle of the 3rd order bright fringe isgiven bysin θ3 = (3)(664×10−9

m)1.20×10−4 m

= 0.0166.

y = L tan θ3 ≈ 4.56 cm

Physics 202 – p. 14/26


Reflection of an interface

When light travels from a medium of lowerindex of refraction to a region of higher indexof refraction, the reflected wave suffers a 1800

phase change.

When light travels from a medium of higherindex of refraction to a region of lower indexof refraction, the reflected wave suffers a nophase change.

Physics 202 – p. 15/26


Reflection of an interface

Physics 202 – p. 16/26


Reflection of an interface: Air Wedge

Physics 202 – p. 17/26



Physics 202 – p. 18/26



Constructive interference:Let d be the thickness of the air gap at anypoint.2 d = (m −

12)λ

m = 1, 2, 3, ..

Destructive interference:2 d = mλm = 1, 2, 3, ..

Physics 202 – p. 19/26


Reflection of an interface: Air Wedge exampleA very fine wire 7.33 × 10−3mm in diameter isplaced between two flat glass plates (see Fig.28-9). Light whose wavelength in air is 600 nmfalls perpendicular to the plates, and a series ofbright and dark bands is seen. How many brightand dark bands will there be? Will the area nextto the wire bright or dark?

(2)(7.33 × 10−3mm)/(6 × 10−7m) = 24.5.Half-integer area next to the wire will bebright.

Total of 25 dark lines and 25 bright lines.

Physics 202 – p. 20/26


Reflection of an interface: Air Wedge exampleA very fine wire 7.33 × 10−3mm in diameter isplaced between two flat glass plates (see Fig.28-9). Light whose wavelength in air is 600 nmfalls perpendicular to the plates, and a series ofbright and dark bands is seen. How many brightand dark bands will there be? Will the area nextto the wire bright or dark?

(2)(7.33 × 10−3mm)/(6 × 10−7m) = 24.5.Half-integer area next to the wire will bebright.

Total of 25 dark lines and 25 bright lines. Physics 202 – p. 20/26


Reflection of an interface: Newton’s ringLike an air wedge

Physics 202 – p. 21/26


Reflection of an interface: Thin Film

Physics 202 – p. 22/26


Reflection of an interface: Thin FilmLet n > 1 be the index of refraction inside the thinfilm of thickness t.

Constructive interference:2 t = (m + 1

2)λvacuum

n

m = 0, 1, 2, ..

Destructive interference:2 t = m λvacuum

n

m = 0, 1, 2, ..

Physics 202 – p. 23/26


Reflection of an interface: Thin Film and color

Physics 202 – p. 24/26


Reflection of an interface: Thin Film with onephase change

Physics 202 – p. 25/26


Reflection of an interface: Thin Film exampleA soap bubble appears green (λ = 540 nm) at apoint on its front surface nearest the viewer.What is its minimum thickness? Assume n = 1.35

Minimum thickness ⇒ m = 0. Here we haveconstructive interference.

t = λ

4 n= 5.4×10−7

m

4×1.35 = 100 nm.

Physics 202 – p. 26/26

Physics 202 - Galileogalileo.phys.virginia.edu/~pqh/202_17n.pdfPhysics 202 – p. 20/26 Interference...

Documents

Transcript of Physics 202 - Galileogalileo.phys.virginia.edu/~pqh/202_17n.pdfPhysics 202 – p. 20/26 Interference...