Diffraction Grating
OBJECT: To determine the wavelength of prominent spectral lines of mercury
light by a plane transmission grating, using normal incidence method.
APPARATUS: Mercury lamp, Spectrometer, diffraction grating, reading lens,
torch.
FORMULA USED: The wavelength of any spectral line can be obtained from the
formula.
(a + b) sinθ = nλ
or, λ = ((a + b) sinθ) / n
where, a + b = Grating element
θ = Angle of diffraction
n = Order of principal maxima
THEORY: Diffraction grating is an optical component having a periodic structure
which can split and diffract several light beams travelling in different directions.
light. At normal incidence, 𝑆𝑖𝑛𝜃 = 𝑁𝑛𝜆 where, N is the number of lines per unit
This depends on the spacing of the grating and the wavelength of the incident
length of the grating, n is the order of the spectrum, λ is the wavelength of light
and θ is the diffraction angle.
The preliminary adjustments of the spectrometer are made. The grating is set for
normal incidence. The slit is illuminated by mercury vapour vamp. The telescope
is brought in a line with the collimator and the direct image of the slit is made to
coincide with the vertical cross wire. The readings of one vernier are noted. The
vernier table is firmly clamped. Now, the telescope is rotated exactly through 90°
and is fixed in this position. The grating is mounted vertically on the prism table
with its ruled surface facing the collimator. The vernier table is released and is
slowly rotated till the reflected image coincides with the vertical cross wire. The
leveling screws are adjusted so that the image is at the centre of the field of view
of the telescope. The prism table is fixed and after making fine adjustments with
the tangential screw, the readings of the vernier are noted. Now, the angle of
incidence is 45°. The vernier table is then released and rotated exactly through
45° in the proper direction so that the surface of the grating becomes normal to
the incident light. The vernier table is firmly clamped in this position.
The telescope is then released and is brought to observe the direct image. On
the either side of the direct image, the diffraction spectra are seen.The telescope
is turned slowly towards the left so that the vertical cross wire coincides with the
violet lines of the first order. The readings of the vernier are taken. The vertical
cross wire is then made to coincide with the other lines on the left and the vernier
readings are taken in each case. The telescope is then moved to the right and the
reading of different lines is similarly taken. The difference between the readings
on the left and right on the same vernier is determined for each line. The mean
value of this difference gives 2θ-twice the angle of diffraction. Thus the angle of
diffraction θ for each spectral line is determined. The wavelength of the green line
is 546.1 x10-9m. The number of lines per meter (N) of the grating is calculated.
Using this value of N, the wavelengths of the other prominent lines in this
spectrum are calculated.
PROCEDURE:
I. The telescope is rotated on one side (say left) of the direct image till red
line of the first order spectrum comes on the cross wire (fig5). The
readings of both the verniers are recorded. Similarly, readings of both the
verniers are recorded for other spectral lines (say yellow and violet).
II. Now rotate the telescope on the other side of the direct image and repeat
the same procedure as above.
III. Find out the difference in readings of the same kind of verniers for each
spectral line and calculate angle of diffraction.
OBSERVATIONS:
L.C. = (20 min / 60) = 1/3 min = 20 sec. Keeping the L.C. = 1/3 min is convenient
for calculations.
Observations for the grating element:
Number of lines per inch on the grating = …………..
Grating element (a + b) = 2.54 cm / number of lines per inch
Observations for angle of diffraction:
𝑀𝑒𝑎
𝑛𝜃
Spectral Vernier Reading on LHS Reading on RHS 2𝜃
reading − 𝑉) (°)
line MSR CVSR Total MSR CVSR Total = (𝑈
reading
U( °) V(°) (°)
I order
V1
Red
V2
V1
Yellow
V2
green V1
V2
CALCULATIONS:
λ = ((a + b) sinθ) / n
RESULTS:
Violet line λv = …………… Å
Yellow Line λy = …………… Å
Red Line λr = …………… Å
PRECAUTIONS:
i. The grating should not be touched with hand or rubbed. It should always
be held by means of fingers kept on the opposite edges of the grating.
ii. Grating should be perfectly normal to the axis of the collimator.
iii. The turn – table must be leveled optically.
iv. While recording observations the telescope should be rotated in the same
direction in order to avoid backlash error.
v. The slit should be as narrow as possible.
vi. All the preliminary adjustments of the spectrometer must be made before
starting the experiment.
vii. While taking observations the turn table must remain clamped.
viii. Both verniers should be read.
Sources of error:
i. The spectrometer is not properly adjusted.
ii. Error may be due to parallax.
iii. If the reading is not taken overhead the spectrometer. 9. Reading may not
be taken taking care of precautions.
