Hence, we have s= nDλ/a
Consider the nth and the (n+1)th ringes,
Fringe separation y= s -s =Dλ/a --> λ= ay/D
Therefore, the wavelength λ can be estimated if fringe separation y is measured.
Using a plane diffraction grating
A diffraction grating consists of evenly separated opaque and
transparent parallel lines. The diffracted light from transparent
lines interfere to give diffraction pattern which consists of
evenly separated bright fringes.
Fig 2 shows parallel light being diffracted at an angle θ
by the diffraction grating:
Bright fringes occur at positions where constructive interference occurs. The path difference x between light diffracted from successive transparent lines is a multiple n of the wavelength λ:
x= d sinθ = nλ, where n=0,1,2,3… is known as order number.
If we can measure the angle of diffraction for the first order bright fringe, wavelength of the light source can be estimated using the formula λ= d sinθ.
Procedure
Using a double-slit
- The laboratory was blacked out. The apparatus was set up as shown in Fig.3. 2 shutter holes were on the compact light source. The one through which the filament of the lamp inside was seen as a short vertical line was opened. That hole towards the double-slit was pointed.
- The separation of n fringes was marked on the translucent screen. Aided by a magnifying glass, the fringe separation y was measured with a millimeter scale.
- Aided by a magnifying glass, the slit separation a was measured with a millimeter scale.
- The slit-to-screen distance D with a metre rule was measured.
- The wavelength of light using the formula λ=ay/D.
- The experiment was repeated several times using different slit-to-screen distances.
Using a plane diffraction grating
- A ‘T’ with 2 metre rules was formed
and it was pointed towards
a ray-box 1 to 2 metres away (Fig 4).
- A diffraction grating was held against one end of a metre rule. The vertical filament of the ray-box lamp was viewed through the grating. A diffraction pattern consisting of the first and second order spectra would be seen.(Fig 5)
- A pencil was moved along the second metre rule until it was in line with the middle of the blue colour of the first order spectrum. The distance x was measured.
- From x, tanθ and then sinθ were found. The grating formula λ=dsinθ was applied to calculate the wavelength of the light.
- Steps 9 and 10 were repeated with the green and red colours in turn and the wavelength of the different colours were calculated.
Results and discussion
Using a double-slit
- Calculate the wavelength of light using the formula λ=ay/D.
Slit separation a = 0.3 mm
- How does the slit-to-screen distance D affect the fringes projected on the screen?
As y=λD/a, when the slit-to-screen distance D increases, and wavelength λ and slit separation a remain unchanged, the fringe separation y will increase also.
Using a plane diffraction grating
- Tabulate the results:
For a grating of 3000 lines per cm,
Grating separation d=(1/3000) cm=3.33x10
- Comment on your results. What are the major sources of error?
By calculation, the wavelengths of blue, green and red light are about 500nm, 550nm and 700nm respectively. The official values for them are 450-495nm, 495-570nm and 620-750nm respectively, which are pretty close to the calculated values.
The major sources of error are as follows.
For the double-slit experiment,
-The double slit is not exactly perpendicular to the table surface. The intensity of the fringe pattern are decreased.
-As the intensity of the fringes is low, it is difficult to locate the exact location where destructive interference occurs. This will lead to inaccurate reading of vernier caliper. It can be modified by darkening the place for experiment.
-There are errors from fringe separation reading using vernier caliper.
Maximum error = 0.1/2=0.05mm
For example, the first reading of y is actually 0.85+0.1mm
So the wavelength obtained is not accurate.
For the diffraction grating experiment,
-It is difficult to locate the exact fringe for that particular colour.
-There are errors from readings of x using a metre rule.
Maximum error = 0.1/2=0.05cm
Reading of x for 1st order green fringe is actually 0.17+0.001m
So the wavelength obtained is not accurate.
- In this experiment, the first order spectrum is used foe measuring he wavelengths of different colors. Give one advantage and disadvantage of using the second order spectrum instead.
The advantage is that the angular separation of second order is larger than that of first order. It will have a smaller measurement percentage error.
The disadvantage is that the intensity of the second order is lower and the corresponding fringes for each colour are difficult to locate.
Safety precaution
-The light source is very hot. Hold it with care.
Reference
Tao, Lee & Mak’s A-Level Practical Physics Third Edition (Oxford).P.72-75
