Name: / ______/ Subject: / AL Practical Physics
Date: / ______/ Mark: / ______
Estimating the wavelength of light using a double-slit
and a plane diffraction grating (TAS)
Objective
n To project a Young’s interference pattern on a screen and make measurements to estimate the wavelength of light.
n To estimate the wavelengths of the different colours of the spectrum produced using a fine diffraction grating.
Apparatus
o Double-slit mounted on a large cardboard
o Translucent screen (ground glass or tracing paper)
o Compact light source
o Low voltage power supply
o Magnifying glass
o Metre rule (2)
o Millimeter scale
o Diffraction grating (3000 lines per cm)
o Ray-box (without lens and slit plate)
Theory
Using a double-slit
In the Young’s double slit experiment, two rays through the slits interfere to give the interference pattern. Bright fringes occur at positions where constructive interference occurs. The path difference from the slits at an angle q is a multiple n of the wavelength l, i.e.
a sinq = nl, (where n = 1, 2, 3 ….. is known as order number)
For small value of q,
where s is the distance of the fringe from the central line and D is the distance from the screen to the double slits.
Hence we have .
Consider the nth and (n+1)th fringes,
Fringe separation
Therefore, the wavelength l 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.
The figure shows parallel light being diffracted at an angle q 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 l:
x = d sinq = nl 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 l = d sinq.
Procedure
Using a double-slit
1.
Black out the laboratory. Set up the apparatus as shown. There are 2 shutter holes on the compact light source. Open the one through which the filament of the lamp inside is seen as a short vertical line. Point this hole towards the double-slit.
2. Mark on the translucent screen the separation of n fringes. Aided by a magnifying glass, measure the fringe separation y with a millimeter scale.
3. Aided by a magnifying glass, measure the slit separation a with a millimeter scale.
4. Measure the slit-to-screen distance D with a metre rule.
5. Calculate the wavelength of light using the formula .
6. Repeat the experiment several times using different slit-to-screen distances.
Using a plane diffraction grating
7.
Form a ‘T’ with 2 metre rules and point it towards a ray-box 1 to 2 metres away.
8. Hold a diffraction grating against one end of a metre rule. View the vertical filament of the ray-box lamp through the grating. A diffraction pattern consisting of the first and second order spectra will be seen.
9. Ask your partner to move a pencil along the second metre rule until it is in line with the middle of the blue colour of the first order spectrum. Measure the distance x.
10. From x, find tanq and then sinq. Apply the grating formula l = d sinq to calculate the wavelength of the light.
11. Repeat steps 9 and 10 with the green and red colours in turn and calculate the wavelength of the different colours.
Results and discussion
Using a double-slit
12 Calculate the wavelength of light using the formula l= .
Slit separation a = 0.24mm
Fringe separation y/mm / 6.5 / 7 / 9.2 / 2.75Slit-to-screen distance D/m / 2.15 / 2.49 / 3.16 / 0.93
Wavelength l = /m / 7.26x10-7 / 6.75x10-7 / 6.99x10-7 / 7.10x10-7
Average Wavelength = 7.025x10-7m
13 How does the slit-to-screen distance D affect the fringes projected on the screen?
The larger the slit-to-screen distance, the wider the fringes separation.
Using a plane diffraction grating
14. Tabulate the results:
For a grating of 3000 lines per cm,
Grating separation d = 1/3000 cm = 3.33 ´ 10–6 m
Colour / Blue / Green / Redx/m
tan q
sin q
l = d sin q /m
15 Comment on your results. What are the major sources of error?
It is difficult to move the pencil to the middle of the colour lines accurately.
The reading error of the ruler.
The ruler is not parallel to the spectrum.
16 In this experiment, the first order spectrum is used for measuring the wavelengths of different colors. Give one advantage and one disadvantage of using the second order spectrum instead.
The distance of the colour line from centre is larger, so the percentage error of the reading
of the ruler will be smaller.
However, the colour lines are dimmer, it is more difficult the see.
- 6 -