Lecture 21Wave Optics-2 Chapter 22

PHYSICS 270Dennis Papadopoulos

March 31, 2010

White light passes through a diffraction grating and forms rainbow patterns on a screen behind the grating. For each rainbow,

A. the red side is farthest from the center of the  screen, the violet side is closest to the center.

B. the red side is closest to the center of the screen,  the violet side is farthest from the center.

C. the red side is on the left, the violet side on  the right.

D. the red side is on the right, the violet side on  the left.

€

Δy ~ λL /d

Two slit and five slit diffraction

653 nm with 150 slits

Single Slit Diffraction

a<

€

Δr12 =a

2sinθ1 = λ /2

Same for 3 - 4 and 5 - 6 destructive interference

Pair wavelets with extra distance traveled

Pair wavelets with extra distance traveled etc€

asinθ p = pλ , p =1,2,..

θ p ≈ p(λ /a)Angles of dark fringes

€

asinθ p = pλ , p =1,2,..

θ p ≈ p(λ /a)

Angles of dark fringes

Positions on the screen

€

y p = L tanθ p ≈ Lθ p =

= pLλ

a

w = 2Lλ

a

The figure shows two single-slit diffraction patterns. The distance between the slit and the viewing screen is the same in both cases. Which of the following could be true?

A. The wavelengths are the same for both; a1 > a2.

B. The wavelengths are the same for both; a2 > a1.

C. The slits and the wavelengths are the same for both; p1 > p2.

D. The slits and the wavelengths are the same for both; p2 > p1.

A. The wavelengths are the same for both; a1 > a2.

B. The wavelengths are the same for both; a2 > a1.

C. The slits and the wavelengths are the same for both; p1 > p2.

D. The slits and the wavelengths are the same for both; p2 > p1.

The figure shows two single-slit diffraction patterns. The distance between the slit and the viewing screen is the same in both cases. Which of the following could be true?

Light decides to take the path of “least time” which turns out to be given by the reflection law.But how does it find this path? Does it check all other paths? Does it smell the nearby paths and checks them against each other?The answer is in a way yes. The “smelling instrument” is the wavelength and the decision process is interference.

In fact light follows all possible paths that first reflect on the mirror and reach point P.However we must keep not only the amplitude but also the phase and then add the result as vectors

Light goes from S through the mirror to P with the same amplitude through all paths but with different phase since the lengths of the paths are different

S P

S P

L

y

Δ

€

Δφ ≈2πyΔ

Lλminimum mirror size → Δφ = π

Δ ≈Lλ

2y

What is the minimum size of a mirror to give reflection?

The ends of he mirror not important

y

L

/ 2

( / )

y d

Ly L y

Δ

Δ

Δy ->Minimum size of the mirror

Notice that ≈.3-.6 microns

The Diffraction GratingSuppose we were to replace the double slit with an opaque screen that has N closely spaced slits. When illuminated from one side, each of these slits becomes the sourceof a light wave that diffracts, or spreads out, behind the slit. Such a multi-slit device is called a diffraction grating. Bright fringes will occur at angles θm, such that

The y-positions of these fringes will occur at

rays

€

Dc = 2.4λL

D

L

Single slit diffraction

When laser light shines on a screen after passing through two closely spaced slits, you see

A. a diffraction pattern.B. interference fringes.C. two dim, closely spaced points of light.D. constructive interference.

A. a diffraction pattern.B. interference fringes.C. two dim, closely spaced points of light.D. constructive interference.

When laser light shines on a screen after passing through two closely spaced slits, you see

Circular-Aperture DiffractionLight of wavelength λ passes through a circular aperture of diameter D, and is then incident on a viewing screen a distance L behind the aperture, L>>D. The diffraction pattern has a circular central maximum, surrounded by a series of secondary bright fringes shaped like rings.The angle of the first minimum in the intensity is

The width of the central maximum on the screen is

Tactics: Choosing a model of light

€

w = 2.44λL /D

2.44λL /Dc = Dc

Dc = 2.44λL

≈ nmL≈1 m