Brainscape's Knowledge GenomeTM


Top Flashcards (Certified)
All Flashcards

Fourier and Optics > Diffraction > Flashcards

Diffraction Flashcards

1
Q

What is diffraction?

A

The process where light spreads when it passes through a narrow aperture.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

When is light diffracted?

A

If the physical size of the aperture is comparable to, or smaller than, the wavelength of the light

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is Fraunhofer Diffraction?

A

Waves incident on and leaving the aperture can be considered plane

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is Fresnel Diffraction?

A

Waves incident on and leaving the aperture can NOT be considered plane

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What is the geometry for observing Fraunhofer diffraction?

A
  • Large distances between S(source) and screen and also the screen and L(second screen)
    ^ Too big of a system over come by:
    OR
  • Two lenses to produce incoming and outgoing plane waves ( diffraction pattern is produced in focal plane of second lens) – at a distance f from L
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What are the steps of calculating Fraunhofer diffraction produced by an (1D) aperture?

A
  • Write f(x) (describes the transmission of light through the screen)
  • Calculate the Fourier transform of f(x) to give F(kx)
  • Calculate |F(kx)|^2
    Substitute kx =2Ο€sintheta/lambda
    Replace sintheta with x/f

Fraunhofer diffraction by a single long square slit:
𝐼(π‘₯)=𝐼_0 sinc ^2 (πœ‹π‘€x/π‘“πœ†)
Fraunhofer diffraction by a single long triangle slit:
𝐼(π‘₯)=𝐼_0 sinc ^4 (πœ‹π‘€x/π‘“πœ†)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

How do we get a aperture that has a variable value?

A

Systems with transmission functions intermediate between one and zero
For example using glass with filter, if it is very thin it will partial transmit light. Used in photography

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What does the diffraction depend on?

A
  • Depends on the size of the aperture.
  • aperture size&raquo_space; wavelength
  • light travels in a straight line with no diffraction as a result we get geometrical optics and shadows etc
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is the width of the central peak of the diffraction pattern by a single slit?

A

Ξ”x=2sΞ»/w ( s or f )
Example 15

Ξ”x -the separation between fringes 
s - the separation between screens 
f - distance to screen L when a lens is used
Ξ» - wavelength
w - the slit width
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What are the steps of calculating Fraunhofer diffraction produced by an (2D) aperture?

A
  • Write f(x) (describes the transmission of light through the screen)
  • Calculate the Fourier transform of f(x) to give F(kx)= 𝐹(π‘˜_π‘₯,π‘˜_𝑦)=1/√2πœ‹ 1/√2πœ‹ ∫(βˆ’βˆž)^(+∞)∫(βˆ’βˆž)^(+∞)𝑓(π‘₯,𝑦)𝑒^(βˆ’π‘–π‘˜_π‘₯ π‘₯) 𝑒^(βˆ’π‘–π‘˜_𝑦 𝑦) dπ‘₯d𝑦 (In 2D)
  • Calculate |F(kx)|^2
    Substitute kx =2pisintheta/lambda
    Replace sintheta with x/f
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What are the equations for the diffraction by a rectangular aperture?

A 
Ξ”x=2sΞ»/wx
Ξ”y=2sΞ»/wy
( s turns into f for a lens)
Ξ”x - the spot size (the diameter of the central maxima of diffraction pattern) 
s - the separation between screens 
Ξ» - wavelength
w - the slit width/size of the aperture
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What are the equations for the diffraction by a circular aperture?

A

Ξ”x =~2.44Ξ»s/D
( s turns into f for a lens)
Ξ”x - the spot size (the diameter of the central maxima of diffraction pattern)
s - the separation between screens
f - focal length/distance to screen L when a lens is used
Ξ» - wavelength
w - the slit width

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What are the effects of diffraction on spatial resolution of a telescope?

A

Diffraction as light passes through a telescope may prevent closely spaced objects from being separately resolved.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What are the equations for the diffraction by two very narrow slits?

A 
Fridge spacing:
Ξ”x =Ξ»s/d (s or f)
s - the separation between screens 
f - distance to screen L when a lens is used
Ξ» - wavelength
d - the separation between slits 
Ξ”x -the separation between fringes
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What are the equations for the diffraction by two slits of non-zero width?

A

𝐼(π‘₯)=𝐼_0 sinc ^2 (πœ‹π‘€/π‘“πœ† π‘₯) cos^2⁑(πœ‹π‘‘/πœ†π‘“ π‘₯)
First term - Diffraction by a single slit
Second term - Diffraction by two
very narrow slits

IGNORING THE FIRST TERM
Intense maxima occur when denominator term is zero which gives Ξ”x =Ξ»s/d, we maximise d by choosing the one at the very end d = N-1/2 * centre of slit spacing

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the consequence of diffraction by two slits of non-zerowidth?

A

Missing bright fridges in the diffraction pattern (missing orders)

17
Q

What are the equations for diffraction by an array of N identical slits?

A

𝐼(π‘₯)=𝐼_0sinc^2 (πœ‹π‘€x/πœ†π‘“) (sin⁑(π‘π‘‘πœ‹x/πœ†π‘“)/sin⁑(π‘‘πœ‹x/πœ†π‘“ )^2

First Term - Diffraction by a single slit
Second Term - Diffraction by a N very narrow slits

IGNORING THE FIRST TERM
Intense maxima occur when denominator term is zero this gives the diffraction equation

Weaker maxima occur when numerator equals one

18
Q

What is the diffraction equation and what does it tell us?

A

𝑑 sinβ‘πœƒ=π‘›πœ†
(for large N)
Tells us the angles where intense light is diffracted.

19
Q

What is the equation for the angular width of the main maxima of the diffracted light?

A

Ξ”πœƒ=πœ† 2πœ‹/(π‘‘πœ‹ cosβ‘πœƒ )𝑁

20
Q

What is the equation for the number of diffraction orders produced by a diffraction grating?

A

nmax= d/πœ†

n must be integer it must take the next lowest whole number

21
Q

What is the Rayleigh criterion for spectral resolution?

A

When the maxima of one wavelength coincides with the first minima of the second wavelength

22
Q

What is the equation for the spectral resolving power?

A

πœ†/Ξ”πœ†
πœ† - average wavelength
Ξ”πœ† - the difference between two wavelength

23
Q

What is a diffraction grating and why is it used?

A

A structure consisting of a large number of slits (e.g. N>100)

used to split light consisting of many wavelengths into the wavelength components

24
Q

What is the equation for the spectral resolving power for a diffraction grating?

A 
πœ†/Ξ”πœ†=𝑛𝑁
n - diffraction order
N - slit number
πœ† - average wavelength
Ξ”πœ† - the difference between two wavelength
25
Q

What are the consequences of diffraction?

A

When light of wavelength passes through the aperture of a telescope of diameter D and if the focal length is f then the angular and spatial widths of the maximum of the resultant diffraction pattern are

Ξ”πœƒβ‰ˆ2.44 πœ†/𝐷, Δπ‘₯β‰ˆ2.44 πœ†π‘“/𝐷

If light from two closely spaced objects enters a telescope the spread in their images that results from diffraction may prevent them from being separated – spatially resolved

There will be a minimum angular separation that two objects can have such that the telescopes shows them as being separate – this is the angular resolution of the system

26
Q

What is the equation for the size of an image if diffraction is IGNORED and not ignored?

A

Ξ”π‘₯ = Ξ±f
Ξ± - angular power
f - focal length

Ξ”π‘₯β‰ˆ2.44 πœ†π‘“/𝐷
πœ† - wavelength
𝑓 - focal length
D - diameter

If 2nd effect&raquo_space; 1st so just use 2nd effect

27
Q

What is the angular resolution of an optical system/resolving power of a telescope?

A

Ξ” Ξ± = 1.22πœ†/𝐷

Ξ” Ξ± - resolving power
D - input aperture diameter
πœ† - imaging light of wavelength

28
Q

What is the equation for the maximum distance an optical system can resolve light?

A

Ξ” Ξ± = x/d

x- separation
d - min distance
Ξ± - angular resolving power (minimum angular separation between two points)

Fourier and Optics (4 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2025 Bold Learning Solutions. Terms and Conditions