Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

6 Questions for Assignment 6 - Physical Optics | 1051 455, Assignments of Typography

Material Type: Assignment; Class: 1051 - Physical Optics; Subject: Imaging Science; University: Rochester Institute of Technology; Term: Spring 2008;

Typology: Assignments

2009/2010

Uploaded on 03/28/2010

koofers-user-g8y
koofers-user-g8y 🇺🇸

5

(2)

10 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
1051-455-20073 Homework #6
Read P3§9 Coherence and P3§11 Frau nh of er Diraction
Due 16 May 2008 (Th) —: Write up ONE lab of your choice in the “long format” (including abstract,
data, analysis, etc., as listed in the handout)
Due 8 May 2008 (Th) Do the following problems; SHOW YOUR WORK
1. “White” light includes equal “amounts” of each wavelength in the interval 400 nm λ700 nm.
(a) Determine the frequency bandwidth for this wavelength range
(b) Compute the associated coherence time and coherence length of white light.
2. The range of angular temporal frequencies by a light source is ω:
(a) Find the expression for ν
(b) Derive the expression for the corresponding linewidth λ
(c) Derive the expression for the cohe rence le ngt h of the source.
(d) Find the coherence length of a sodium arc that emits two narrow spectral lines:
ω1=3.195 ×1015 radians
sec
ω2=3.198 ×1015 radians
sec
(e) Find the coherence length of a He:Ne “greenie” laser with
ω1=3.171 ×1015 radians
sec
ω2=3.469 ×1015 radians
sec
3. Determine the linewidth in nanometers and in Hertz for laser light whose coherence length is 10 km if
the mean wavelength is 632.8nm (He:Ne)
4. Michelson found that the cadmium red line (λ0= 643.8nm) was the best available light source for
his interference experiment. With it, he could see fringes for optical path dierences up to 300 mm.
Estimate the linewidth λand coherence time tof this light source.
5. A light source emits two wavelengths λ1and λ2. The light is incident upon a binary (composed of
regions that are perfectly transparent or perfectly opaque) f[x, y ]. The light then propagates to an
observation screen located at a very large distance Lfrom the object. Describe and give reasons for
the qualitative appearanceof the observed patterns for the following objects; you may also describe the
patterns quantitatively for extra credit.
(a) fa[x, y]is a single very small transparent aperture (“hole”)
(b) fb[x, y]consists of two apertures that are very narrow along the xaxis and infinitely long along
the yaxis and that are separated by dunits.
(c) fc[x, y]consists of an infinite number of apertures from part bthat are uniformly spaced at
increments of dunits.
MORE→→→
1
pf2

Partial preview of the text

Download 6 Questions for Assignment 6 - Physical Optics | 1051 455 and more Assignments Typography in PDF only on Docsity!

1051-455-20073 Homework

Read P^3 §9 Coherence and P^3 §11 Fraunhofer Diffraction

Due 16 May 2008 (Th) —: Write up ONE lab of your choice in the “long format” (including abstract, data, analysis, etc., as listed in the handout)

Due 8 May 2008 (Th) — Do the following problems; SHOW YOUR WORK

  1. “White” light includes equal “amounts” of each wavelength in the interval 400 nm ≤ λ ≤ 700 nm.

(a) Determine the frequency bandwidth for this wavelength range (b) Compute the associated coherence time and coherence length of white light.

  1. The range of angular temporal frequencies by a light source is ∆ω:

(a) Find the expression for ∆ν (b) Derive the expression for the corresponding linewidth ∆λ (c) Derive the expression for the coherence length ∆c of the source. (d) Find the coherence length of a sodium arc that emits two narrow spectral lines:

ω 1 = 3. 195 × 1015

radians sec ω 2 = 3. 198 × 1015

radians sec

(e) Find the coherence length of a He:Ne “greenie” laser with

ω 1 = 3. 171 × 1015

radians sec ω 2 = 3. 469 × 1015 radians sec

  1. Determine the linewidth in nanometers and in Hertz for laser light whose coherence length is 10 km if the mean wavelength is 632 .8 nm (He:Ne)
  2. Michelson found that the cadmium red line (λ 0 = 643.8 nm) was the best available light source for his interference experiment. With it, he could see fringes for optical path differences up to 300 mm. Estimate the linewidth ∆λ and coherence time ∆t of this light source.
  3. A light source emits two wavelengths λ 1 and λ 2. The light is incident upon a binary (composed of regions that are perfectly transparent or perfectly opaque) f [x, y]. The light then propagates to an observation screen located at a very large distance L from the object. Describe and give reasons for the qualitative appearanceof the observed patterns for the following objects; you may also describe the patterns quantitatively for extra credit.

(a) fa [x, y] is a single very small transparent aperture (“hole”) (b) fb [x, y] consists of two apertures that are very narrow along the x−axis and infinitely long along the y−axis and that are separated by d units. (c) fc [x, y] consists of an infinite number of apertures from part b that are uniformly spaced at increments of d units. MORE→→→

  1. The light diffracted by an object of the form f [x, y] and observed at a distance z 1 in the Fraunhofer diffraction region has the “shape” of the squared magnitude of the Fourier transform of the object after appropriate rescaling of the coordinates back to the space domain

g [x, y] ∝ |F [ξ, η]|^2

ξ→ (^) λ 0 xz 1 ,η→ (^) λ 0 yz 1

where the 2-D Fourier transform is defined:

F [ξ, η] ≡ F 2 {f [x, y]} ≡

Z Z +∞

−∞

f [x, y] exp [− 2 πi (ξx + ηy)] dx dy

The object f [x, y] satisfies the following conditions:

f [x, y] = 1 if |x| ≤ 1 AND |y| ≤ 1 f [x, y] = 0 f [x, y] = 1 otherwise

(a) Sketch f [x, y]; (b) Calculate the diffraction pattern in the Fraunhofer diffraction region if f [x, y] is illuminated by light with wavelength λ 0 ; (c) Sketch the x-axis profile of the diffraction pattern including labels of the values on both axes.