# Fraunhofer Single Slit

Content . 301302303304 .

- Fraunhofer Diffraction Pdf
- Fraunhofer Diffraction At A Single Slit
- Fraunhofer Diffraction Pattern Single Slit
- Fraunhofer Diffraction Class 12
- Fraunhofer Diffraction Formula

S E C T I O N 3 8 . 2 • Diffraction Patterns from Narrow Slits

Fraunhofer DiffractionChapter 11. Fraunhofer Diffraction Last lecture. Numerical aperture of optical fiber. Allowed modes in fibers. Attenuation. Modal distortion, Material dispersion, Waveguide dispersion This lecture. Diffraction from a single slit. Diffraction from apertures: rectangular, circular. Resolution: diffraction limit. Fraunhofer Diffraction by single slit,diffraction of light waves and polarization,resolving power.

**1209**

**Quick Quiz 38.1**

Suppose the slit width in Figure 38.6 is made half as wide.

The central bright fringe (a) becomes wider (b) remains the same (c) becomes narrower.

**Quick Quiz 38.2**

If a classroom door is open slightly, you can hear sounds

coming from the hallway. Yet you cannot see what is happening in the hallway. Why is

there this difference? (a) Light waves do not diffract through the single slit of the open

doorway. (b) Sound waves can pass through the walls, but light waves cannot. (c) The

open door is a small slit for sound waves, but a large slit for light waves. (d) The open

door is a large slit for sound waves, but a small slit for light waves.

θ

sin

dark

= 2

/*a*

sin

dark

=

/*a*

sin

dark

= –

/*a*

sin

dark

= –2

/*a*

*L*

*a*

0

2

*y*

1

*– y*

1

*– y*

2

Viewing screen

θ

θ

θ

θ

λ

λ

λ

λ

**Figure 38.6 **Intensity distribution for a

Fraunhofer diffraction pattern from a

single slit of width *a*. The positions of two

minima on each side of the central

maximum are labeled. (Drawing not to

scale.)

Example 38.1 **Where Are the Dark Fringes?**

Light of wavelength 580 nm is incident on a slit having a

width of 0.300 mm. The viewing screen is 2.00 m from the

slit. Find the positions of the first dark fringes and the width

of the central bright fringe.

**Solution **The problem statement cues us to conceptualize

a single-slit diffraction pattern similar to that in Figure 38.6.

We categorize this as a straightforward application of our

discussion of single-slit diffraction patterns. To analyze the

problem, note that the two dark fringes that flank the

central bright fringe correspond to *m *' # 1 in Equation

38.1. Hence, we find that

From the triangle in Figure 38.6, note that tan !

dark

'

*y*

1

/*L*.

Because !

dark

is very small, we can use the approximation

sin !

dark

## Fraunhofer Diffraction Pdf

! tan !

dark

; thus, sin !

dark

! *y*

1

## Fraunhofer Diffraction At A Single Slit

/*L. *Therefore, the

positions of the first minima measured from the central axis

are given by

The positive and negative signs correspond to the dark

fringes on either side of the central bright fringe. Hence,

the width of the central bright fringe is equal to 2

'*y*

1

' '

7.74 & 10

'

3

m '

To finalize this problem,

7.74 mm.

#

3.87 & 10

'

3

m

'

*y*

1

! *L* sin !

dark

'

(2.00 m)(#1.933 & 10

'

3

)

sin !

dark

' #

%*a*

' #

5.80 & 10

'

7

m

0.300 & 10

'

3

m

' #

1.933 & 10

'

3

note that this value is much greater than the width of the

slit. We finalize further by exploring what happens if we

change the slit width.

What If?

What if the slit width is increased by an order

of magnitude to 3.00 mm? What happens to the diffraction

pattern?

**Answer **Based on Equation 38.1, we expect that the angles

at which the dark bands appear will decrease as *a *increases.

Thus, the diffraction pattern narrows. For *a *' 3.00 mm, the

sines of the angles !

dark

for the *m *' # 1 dark fringes are

The positions of the first minima measured from the central

axis are given by

and the width of the central bright fringe is equal to 2

'*y*

1

' '

7.74 & 10

'

4

m ' 0.774 mm. Notice that this is *smaller *than

the width of the slit.

In general, for large values of *a*, the various maxima and

minima are so closely spaced that only a large central bright

area resembling the geometric image of the slit is observed.

This is very important in the performance of optical instru-

ments such as telescopes.

' #3.87 & 10

'

4

m

*y*

## Fraunhofer Diffraction Pattern Single Slit

1

! *L* sin !

dark

'

(2.00 m)(#1.933 & 10

'

4

)

sin !

dark

' #

%*a*

' #

5.80 & 10

'

7

m

3.00 & 10

'

3

m

' #

1.933 & 10

'

4

## Fraunhofer Diffraction Class 12

Investigate the single-slit diffraction pattern at the Interactive Worked Example link at **http://www.pse6.com.**

**Interactive**