Exp: To measure the wavelength of a monochromatic light source.
Angular position
θr
θr
n=1
Telescope
Turntable
Sodium
Collimator
lamp
n=0
Diffraction
grating
Angular position
θl
Diagram:
Apparatus:
Diffraction Grating, Monochromatic Light Source, Spectrometer
Method:
1. Set up apparatus as shown in diagram.
2. Adjust the spectrometer as follows:
- make sure cross threads are in focus and upright
- focus on a distant object to ensure parallel beams
- illuminate the slit and focus on slit
- adjust the width of the slit to get a narrow beam
- level the turntable
θl
n=1
3. Place the diffraction grating vertically in the holder.
4. Look through the eye-piece which is straight in front of the grating to find the
zero order image. At this stage ensure the vernier scale is zeroed.
5. Move the telescope to the left and right to find the 1st order image.
6. Measure and record the readings on the circular scale/vernier scale.
7. Repeat steps 5 and 6 for the corresponding 1st order image on the right.
8. Repeat steps 5 and 6 and 7 for the second and third order images.
9. Calculate the average value of the wavelength using the formula:
λ = dsinθ
n
λ = wavelength
θ = degrees
n = order image
*****************
d = diffraction grating**********
NB: *(distance between slits) where we have 300 lines per mm, we
have a diffraction grating of 1/300 per mm or 3.33 x 10-6 per
meter.
NB: *(distance between slits) where we have 300 lines per mm, we
have a diffraction grating of 1/300 per mm or 3.33 x 10-6 per
meter.
NB: *(distance between slits) where we have 300 lines per mm, we
have a diffraction grating of 1/300 per mm or 3.33 x 10-6 per
meter.
Precautions
 Make sure diffraction grating is standing vertically
 Ensure turntable is horizontal/flat by using the levlling screws
 Check that the vernier callipers are set at 0 degrees before proceeding
 Adjust the eyepiece until the crossthreads are clearly in focus
 Adjust the slit so that a narrow beam can be seen through the crossthreads
 Check that the central ray is shining directly through the centre of the
crossthreads.
 Set collimeter so that only parallel rays come through
Previous Exam Paper Q’s On This Experiment:
2006
Q2 In an experiment to measure the wavelength of monochromatic light, a narrow beam
of the light fell normally on a diffraction grating. The grating had 300 lines per
millimetre. A diffraction pattern was produced. The angle between the second order
image to the left and the second order image to the right of the central bright image in
the pattern was measured. The angle measured was 40.6°.
 Describe, with the aid of a labelled diagram, how the data was obtained.

How was a narrow beam of light produced?
Adjust the slit in the spectrometer to allow as small a slit as possible.

Use the data to calculate the wavelength of the monochromatic light.
Answer:
λ = dsinθ
n
λ=?
Potential mistake no. 1:
The angle mentioned is 40.6 degrees.
This however is
θ = 20.3°
n=2
Potential mistake no. 2:
d = 1/300 x 10-3 = 3.33 x 10-6 m
λ = (3.33 x 10-6)(sin 20.3°)
2
-6
λ = (3.33 x 10 )(0.3469)
2
-7
λ = 5.78 x 10 m

Explain how using a diffraction grating of 500 lines per mm leads to a more
accurate result.
There would be a greater distance between each image therefore a smaller percentage
error.
 Give another way of improving the accuracy of the experiment.
Repeat experiment a number of times and get the average wavelength.
2002 sample paper
Q2 The following is part of a report given by a student of an experiment to measure the
wavelength of monochromatic light.
“The apparatus was arranged so that a number of bright images could be observed. The
angular position θ for each of these images was determined relative to the central bright
image (n=0). The data obtained are shown in the table. The diffraction grating had 600
lines per mm.”
n
2
1
0
1
2
θ
45.0°
20.4°
0.0°
20.7°
45.2°

Describe, with the aid of a diagram, how the student obtained the above data.

Use the above data to calculate a value for the wavelength of the light.
λ = dsinθ
n
λ=?
d = 1/600 x 10-3 = 1.67 x 10-6
for n = 1: θ = 20.55°
for n = 2: θ = 45.1°
n=1:
λ = (1.67 x 10-6)(sin 20.55°)
1
n=2
λ = (1.67 x 10-6)(sin 45.1°)
2
λ = (1.67 x 10-6)(0.351)
1
λ = (1.67 x 10-6)(0.7083)
2
λ = 5.86 x 10-7m
λ = 5.91 x 10-7m
average
λ = 5.89 x 10-7m

Determine the maximum number of bright images that can be seen using this
diffraction grating.
nmax = dsin90° (sin 90° = 1) => nmax = d
λ
λ
-6
nmax = 1.67 x 10
5.89 x 10-7
nmax = 2.84
nmax = 2
(=> we see 5 bright lines)
 List two factors that affected the accuracy of the experiment.
- if the diffraction grating is not vertical.
- the levelness of the turntable.
Sample Question
3
31.5
2
21.5
Avg 1: 10.55
1
10.6
0
0
1
10.5
Avg 2: 22
2
22.5
3
33
Avg 3: 32.25
Results workings: (Diffraction grating = 300)
d = 1_ = .0033333 per mm = .0033333 = .0003333 per cm
300
10
.0003333 = 3.33 x 10-6 per meter
100
1st order image: 3.33 x 106 sin32.25 = 6.09 x 10-7m
1
2nd order image: 3.33 x 106 sin22 = 6.23 x 10-7m
2
3rd order image: 3.33 x 106 sin32.25 = 5.92 x 10-7m
3
Average Wavelength = 6.08 x 10-7m
Conclusion: To find the wavelength of monochromatic light by using a spectrometer &
the formula: wavelength = dsinθ_
n