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Title: Investigation the interference and diffraction of light of double slit, single slit

and determination of diameter of hair.

Objectives:

-  To measure the distribution intensity and width of a single slit.-  To measure the diffraction pattern of distribution intensity, slit width and the

separation distance of a double slit.

-  To measure the diameter of hair.

Apparatus:

-  HeNe laser, meter ruler, photodiode, ammeter, single slit set, double slit set,

hair.

Introduction:

a)  Single slit

If a light with a wavelength, λ falls onto a very small slit of width, b, then each point

at the slit can be considered as starting point of a spherical wave. The diffraction

pattern is formed on the screen due to interference of the sphere wave. If the pattern is

analyzed according to Fraunhofer approximation, the intensity at point P on the screen,

parallel to the slit is given by:

 [(

) ]

Equation 1

Where θ is the tilt angle from the point connecting the middle of the slit to the center

point of the screen O to a point P, x is the minimum position and s is the distance

between the middle of the slit to the center point of the screen O.

The minimum intensity occurs when:

 

Equation 2

Where a >> x, the minima positions are evenly spaced as θ is small and 

Equation 3

The position of the second maxima is approximately at a half distance between

minima

(

)

Equation 4

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b)  Double slit

The intensity of inference pattern for a small double slit (infinitesimal) is given by:

(

  )Equation 5

where d is the distance between the slits.

The intensity of the diffraction wave by each slit is:

 [( )

]

 Equation 6

The combination of the interference and diffraction effects, results in the double slit

diffraction pattern:

 ( ) [(

) ]

  Equation 7

Experimental method

The HeNe laser (output = 1mW, λ = 632.8nm) was arranged such that the beam was

parallel to the axis of the optical bench and falls on the provided slit as shown in

figure 1. The intensity of light which comes through the slit was measured by aligning

the position of photodiode detector.

i.  For single slit; the intensity distribution was plotted and the width of slit, b

was calculated.

ii.  For double slit; the intensity distribution was plotted, the width of slit, b and

the spacing between the two slits was calculated.

iii.  The same method of the single slit was used to measure the diameter of hair.

Photodiode

Figure 1: The arrangement of the light intensity measurement from a small slit

Laser Meter

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Result:

a)  Single slit

Table 1 : The experimental data for single slit

X (cm) , ∆x = 0.1cm  I (A) , ∆I = 0.001A

-3.5 1.100

-3.0 1.140

-2.5 1.220

-2.0 1.580

-1.5 1.940

-1.0 2.400

-0.5 4.300

0.0 4.400

0.5 4.2401.0 3.000

1.5 1.800

2.0 1.320

2.5 1.160

3.0 1.060

3.5 1.020

b)  Double slit

Table 1 : The experimental data for double slit

X (cm) , ∆x = 0.1cm  I (A) , ∆I = 0.001A

-3.5 1.060

-3.0 1.160

-2.5 1.300

-2.0 1.340

-1.5 1.660

-1.0 1.780

-0.5 4.260

0.0 4.360

0.5 4.320

1.0 2.160

1.5 1.920

2.0 1.680

2.5 1.560

3.0 1.400

3.5 1.260

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c)  Diameter of hair

Table 1 : The experimental data for diameter of hair

X (cm) , ∆x = 0.1cm  I (A) , ∆I = 0.001A

-3.5 1.020-3.0 1.040

-2.5 1.140

-2.0 1.480

-1.5 2.200

-1.0 2.760

-0.5 4.200

0.0 4.340

0.5 4.220

1.0 2.5401.5 1.720

2.0 1.280

2.5 1.000

3.0 0.980

3.5 0.980

Uncertainty

The uncertainty of x and s is 0.1cm while the uncertainty of I is 0.001A.

Data Analysis

The graph 1 shows intensity distribution of light using single slit, graph 2 shows

intensity distribution of light using double slit, while graph 3 shows intensity

distribution of light using hair.

a)  Calculation of the width of single slit

x = distance from the minima to center point

= 2 cm

s = distance between the middle of the slit to the center point

= 55 cm

 

 

 

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Using  

 

 

 

 m

b)  Calculation of the spacing between the two slits

Equation 8

given that d is the slit se paration, θ is the angle from the center of the pattern to themaximum, λ is the wavelength of the light, and m is the order.

x = distance from the center of the pattern to the maximum

= 1.5 cm

s = distance between the middle of the slit to the center point

= 55 cm

 

 

 

 

Using

    

 

 m 

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c)  Calculation of the width of slit of double slit

 

Equation 9

given that b is the slit width, θ is the angle of the first minimum for diffraction, and λ 

is the wavelength of the light, approximation of width of slit of double slit

x = distance from the center of the pattern to the minimum

= 0.5 cm

s = distance between the middle of the slit to the center point

= 55 cm

 

 

 

 

Using  

 

 m

d)  Calculation of the diameter of hair

x = distance from the

minima to center point

= 2 cm

s = distance between the middle of the slit to the center point

= 55 cm

 

 

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Using     

 

 m 

Error Analysis

a)  Uncertainty of the width of single slit

∆θ = ( ) (

) 

=  () (

) 

=  ∆sin θ = √  

= √   

=  

∆b =   =  

=  

Thus, the width of single slit is  m

b)  Uncertainty of the spacing between the two slits

∆θ = ( ) (

) 

=  () (

) 

=  

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∆sin θ = √  

= √   

=

 

∆d =   =  

=  

Thus, the spacing between the two slits  m

c)  Uncertainty of the width of slit of double slit

∆θ = ( ) (

) 

=  () (

) 

=  ∆b =   

=

 

=  

Thus, the width of slit of double slit is  m

d)  Uncertainty of the diameter of hair

∆θ = ( ) (

) 

=  () ( ) 

=  ∆sin θ = √  

= √   

=  

∆b =

  

=  

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=  

Thus, the diameter of hair is  m

Discussion

1.  Light is an electromagnetic wave that has wave properties. Thus it exhibits

some common wave behaviors such as interference and diffraction.

2.  Interference of light is a phenomenon in which two light waves met each other

and combine through superposition to form a resultant light wave of greater or

lower amplitude.

3.  While diffraction of light is the phenomenon that described as the apparent

bending of light waves around small obstacles and the spreading out of light

waves when passing through small openings.

4.  In the experiments, we should use photodiode with very small exposed surface

area to improve the result. This can help to detect the significant change in

light intensity accurately with small change in distance from center point.

5.  We should use high sensitivity ammeter to increase the accuracy of 

experiment. This is because we can detect the small change in current

produced by photodiode and reduce the uncertainty in experiment.

6. 

We should use high power HeNe laser during the experiment. This is becausethe effect of interference and diffraction in light intensity distribution will be

more obvious and significant. Thus, we can obtain more accurate data.

7.  To avoid the experimental error, we should carry out the experiment in a

completely dark room with wide space. This will help to reduce the effect of 

external or reflected light.

8.  To increase the accuracy of data, we should repeat the experiment to obtain

many sets of readings. Hence the effect of random error can be minimized.

Conclusion

In single slit experiment, the value of width of a single slit is  m. While in double slit experiment, the spacing between the two slits  m and the width of slit of double slit is  m.

The diameter of hair calculated is  m.