LAST DANCECHAPTER 26 – DIFFRACTION –

PART II

InstructorCourse

What’s Going On??

Today – Finish (?) Diffraction Tuesday – Nothing – No room is available for a

review session. Wednesday – Examination #4 – Material that we

covered in chapters 24, 25 and 26. Friday – Complete semester’s material. Start

Review Next Monday – Wrap-up and overview of the

course. December 12 - SATURDAY – 9:00AM –

Psychology Building Room PSY 108. BE THERE!!! Last Mastering Physics Assignment Posted. No

more! Ever!

Last Time – Two Slit Interference

sind m

Two small loudspeakers that are 5.50 m apart are emitting sound in phase. From both of them, you hear a singer singing C# (frequency 277 Hz), while the speed of sound in the room is 340 m/s. Assuming that you are rather far from these speakers, if you start out at point P equidistant from both of them and walk around the room in front of them, at what angles (measured relative to the line from P to the midpoint between the speakers) will you hear the sound (a) maximally enhanced? Neglect any reflections from the walls.sin

sin

d m

m

d

340 m/s

f=277Hz

v 340= 1.23

277

v

mf

From another world .. sound.

Table

m sin()=m/d degrees0 0 0

1 0.2236363640.22554

413.2672

8

2 0.4472727270.46371

427.2772

8

3 0.6709090910.73543

443.2608

3

4 0.8945454551.10741

365.1419

55 1.118181818 ? -6 1.341818182 ? -

Diffraction Huygens’ principle

requires that the waves spread out after they pass through narrow slits

This spreading out of light from its initial line of travel is called diffraction In general, diffraction

occurs when waves pass through small openings, around obstacles or by sharp edges

Diffraction Grating

The diffracting grating consists of many equally spaced parallel slits of width d A typical grating contains several thousand

lines per centimeter The intensity of the pattern on the screen

is the result of the combined effects of interference and diffraction

Diffraction Grating The condition for maxima is

d sin θbright = m λ

m = 0, 1, 2, … The integer m is the order

number of the diffraction pattern

If the incident radiation contains several wavelengths, each wavelength deviates through a specific angle

Diffraction Grating, 3 All the wavelengths are

focused at m = 0 This is called the zeroth

order maximum The first order maximum

corresponds to m = 1 Note the sharpness of the

principle maxima and the broad range of the dark area This is in contrast to the

broad, bright fringes characteristic of the two-slit interference pattern

Active Figure: The Diffraction Grating

DIFFRACTION GRATING PATTERN

CD=Diffraction Grating

A shadow isn’t simply a shadow.

But what about this???

What about shadows???

Shadow of a small steel ball Reality

Fringes

Bright Center

This effect is called DIFFRACTION

Diffraction Vs. Interference

Both involve addition of waves from different places and technically, both are the same phenomenon.

Observation requires monochromatic light and a small, coherent light source.

If you are close to a source (non paraxial approx) we call it

Fresnel Diffraction or near-field diffraction. Far away we call it Fraunhofer or far-field diffraction

Diffraction usually refers to a continuous source of wavelets adding up. Interference has a finite number of sources for which the phase is constant over each “source”.

Another case -

Geometrical

Shadow

Adding waves a piece at a time..

D

Single SlitScreen

Maxima

WHY?

Single-Slit Diffraction A single slit placed between a

distant light source and a screen produces a diffraction pattern It will have a broad, intense central

band – central maximum The central band will be flanked by a

series of narrower, less intense secondary bands – secondary maxima

The central band will also be flanked by a series of dark bands – minima

The results of the single slit cannot be explained by geometric optics Geometric optics would say that light

rays traveling in straight lines should cast a sharp image of the slit on the screen

Single-Slit Diffraction

Fraunhofer Diffraction occurs when the rays leave the diffracting object in parallel directions Screen very far from the slit Converging lens (shown)

A bright fringe is seen along the axis (θ = 0) with alternating bright and dark fringes on each side

Single-Slit Diffraction According to Huygens’ principle,

each portion of the slit acts as a source of waves

The light from one portion of the slit can interfere with light from another portion

All the waves that originate at the slit are in phase

Wave 1 travels farther than wave 3 by an amount equal to the path difference δ = (a/2) sin θ

Similarly, wave 3 travels farther than wave 5 by an amount equal to the path difference δ = (a/2) sin θ

Single-Slit Diffraction

If the path difference δ is exactly a half wavelength, the two waves cancel each other and destructive interference results

δ = ½ λ = (a/2) sin θ sin θ = λ / a

In general, destructive interference occurs for a single slit of width a when

sin θdark = mλ / a m = 1, 2, 3, …

Single-Slit Diffraction

A broad central bright fringe is flanked by much weaker bright fringes alternating with dark fringes

The points of constructive interference lie approximately halfway between the dark fringes

ym = L tan θdark , where sin θdark = mλ / a

25. •A beam of laser light of wavelength 632.8 nm falls on a thin slit 0.00375 mm wide. After the light passes through the slit, at what angles relative to the original direction of the beam is it completely cancelled when viewed far from the slit?

27. •Parallel light rays with a wavelength of 600 nm fall on a single slit. On a screen 3.00 m away, the distance between the first dark fringes on either side of the central maximum is 4.50 mm. What is the width of the slit?

30. •Light of wavelength 633 nm from a distant source is incident on a slit 0.750 mm wide, and the resulting diffraction pattern is observed on a screen 3.50 m away. What is the distance between the two dark fringes on either side of the central bright fringe?

35. •A laser beam of wavelength 600.0 nm is incident normally on a transmission grating having 400.0 lines/mm. Find the angles of deviation in the first, second, and third orders of bright spots.

38. •(a) What is the wavelength of light that is deviated in the first order through an angle of 18.0° by a transmission grating having 6000 lines/cm? (b) What is the second-order deviation for this wavelength? Assume normal incidence.

END