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λ of Hg spectrumusing Grating - minimum
deviation by spectrometer
Mrs.P.Kanmani,
Assistant Professor,
Department of Physics,
V.Vanniaperumal Collegefor Women,
Virudhunagar.
λ of Hg spectrumusing Grating - minimum deviation by
spectrometer
Principle:
The phenomenon of spreading out of light waves into the geometrical (dark)
shadow when light passes through a small aperture (or about an obstacle) is
known asdiffraction.
λ of Hg spectrumusing Grating - minimum deviation by
spectrometer
Diffraction Grating:
A diffraction grating consists of a periodic array of a large number of
equidistant slits of width ’b’ which are separated by a distance ’a’ . The period a is
known asthe grating constant.
The diffraction pattern due to a grating is essentially the same as the
diffraction pattern due to M slits, where M is a large number and is obtained by
the superposition of waves emanating from all the slits on the observation plane
λ of Hg spectrumusing Grating - minimum deviation by
spectrometer
Grating equation :
Consider the incidence of plane waves
making an angle θi with the plane of the
grating as shown in Figure. The net path
difference for waves from successive slits is
given by
∆ =∆1 +∆2 =asin θi +asin θ
where θ is the angle corresponding to any
arbitrary direction of the diffracted light.
λ of Hg spectrumusing Grating - minimum deviation by
spectrometer
Grating equation :
For normal incidence θi =0 and therefore
∆ =a sin θ. When ∆ =nλ, where n is an integer,
all diffracted waves in the corresponding direction
θn are in phase, and their amplitudes add up to
give maximum intensity. Thus, we have the
grating equation, which gives the positions of the
intensity maximaas
asin θn =nλ , n =0, ±1, ±2,. .
λ of Hg spectrumusing Grating - minimum deviation by
spectrometer
Diffraction Grating:
λ of Hg spectrumusing Grating - minimum deviation by
spectrometer
Aim :
Todetermine the wavelengths of light emitted by amercuryvapour lampby using
adiffraction grating
Apparatus :
Spectrometer, grating and holder, mercuryvapour lamp, magnifying lens,
Spirit level
λ of Hg spectrumusing Grating - minimumdeviation by
spectrometer
Procedure:
1. Setting the prismtable
The prism table is made horizontal first with the help of a
spirit-level by adjusting the leveling screws D, E and F
To start with, the prism-table is rotated about its axis and
adjusted in such a way that the parallel straight lines
along with the two screws E and F are perpendicular to
the axis joining the collimator and the telescope when they
are aligned. A three way spirit level is kept on the prism
tablewith its edgealongthe parallellines.
λ of Hg spectrumusing Grating - minimumdeviation by
spectrometer
Procedure:
2. Setting up the Spectrometer
Turn on the mercurylamp. Now, look through the eyepieceof the telescope and slide the eyepiecein
and out until the cross-hairs comeinto sharp focus.
Focusthe telescope at infinity by rotating focus knob. This is best accomplishedby focusing on a
distant object(e.g.; out the window).
Now, align the telescope directly opposite the collimator. View the slit through the telescope, rotate
the telescope slightly if necessary, you should seesomelight if the slit is openpartially. Adjust the
focus knob of collimator to makethe sharpimageof the slit. Do not changethe focus of the
telescope. Finally, narrowdown the slit asmuchaspossibleand fine adjust the focus if necessary.
λ of Hg spectrumusing Grating - minimumdeviation by
spectrometer
Procedure:
3. Normal incidence:
Thetelescopeis brought in aline with the collimator and the direct imageof the slit is made
to coincidewith the vertical crosswire. Thereadings of one vernier arenoted. Thevernier
table is firmly clamped. Now, the telescope is rotated exactly through 90° and is fixed in this
position. Thegrating is mounted vertically on the prismtable with its ruled surface facing
the collimator. The vernier table is releasedand is slowly rotated till the reflected image
coincideswith the vertical crosswire. Theleveling screwsareadjusted sothat the imageis at
the centreof the field of view of the telescope.
λ of Hg spectrumusing Grating - minimumdeviation by
spectrometer
Procedure:
3. Normal incidence:
Theprism table is fixed and after making fine adjustments with the tangential screw, the
readingsof the vernier arenoted. Now, the angle of incidenceis 45°. Thevernier table is then
releasedand rotated exactly through 45° in the properdirection sothat the surface of the
grating becomesnormal to the incident light. The vernier table is firmly clamped in this
position.
Thetelescope is then releasedand is brought to observethe direct image. .
λ of Hg spectrumusing Grating - minimumdeviation by
spectrometer
Procedure:
3. Diffraction Pattern
Onthe either side of the direct image,the diffraction spectra areseen.Thetelescope is turned slowly
towards the left sothat the vertical crosswire coincideswith the violet lines of the first order.The
readingsof the vernier aretaken. Thevertical crosswire is then madeto coincide with the other lines
onthe left and the vernier readingsaretaken in eachcase. Thetelescope is then moved to the right
and the readingof different lines is similarly taken.
λ of Hg spectrumusing Grating - minimumdeviation by
spectrometer
Procedure:
3. Diffraction Pattern
Thedifference between the readings on the left and right on the samevernier is determined
for eachline. Themeanvalue of this difference gives 2θ-twice the angleof diffraction. Thus the
angleof diffraction θ for eachspectral line is determined. Thewavelength of the greenline is 546.1
x10-9m. Thenumberof lines permeter(N) of the grating is calculated. Using this value of N, the
wavelengths of the other prominent lines in this spectrum arecalculated.
λ of Hg spectrumusing Grating - minimum deviation by
spectrometer
Formula:
At normal incidence
sin 𝜃 = 𝑁𝑛𝜆
N
𝜃
𝜆
Number of lines/mm in grating
Angle of diffraction in degrees
Wavelength in meters
λ of Hg spectrumusing Grating - minimum deviation by
spectrometer
Tables:
Tofind N
λ of Hg spectrumusing Grating - minimum deviation by
spectrometer
Tables:
λ of Hg spectrumusing Grating - minimum deviation by
spectrometer
λ of Hg spectrumusing Grating - minimum deviation by
spectrometer
Result :
Thewavelength of prominentlines in the mercuryspectrum are
Red
orange------
yellow-------
Green-----
Blue -----
Violet

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Grating.pptx

  • 1. λ of Hg spectrumusing Grating - minimum deviation by spectrometer Mrs.P.Kanmani, Assistant Professor, Department of Physics, V.Vanniaperumal Collegefor Women, Virudhunagar.
  • 2. λ of Hg spectrumusing Grating - minimum deviation by spectrometer Principle: The phenomenon of spreading out of light waves into the geometrical (dark) shadow when light passes through a small aperture (or about an obstacle) is known asdiffraction.
  • 3. λ of Hg spectrumusing Grating - minimum deviation by spectrometer Diffraction Grating: A diffraction grating consists of a periodic array of a large number of equidistant slits of width ’b’ which are separated by a distance ’a’ . The period a is known asthe grating constant. The diffraction pattern due to a grating is essentially the same as the diffraction pattern due to M slits, where M is a large number and is obtained by the superposition of waves emanating from all the slits on the observation plane
  • 4. λ of Hg spectrumusing Grating - minimum deviation by spectrometer Grating equation : Consider the incidence of plane waves making an angle θi with the plane of the grating as shown in Figure. The net path difference for waves from successive slits is given by ∆ =∆1 +∆2 =asin θi +asin θ where θ is the angle corresponding to any arbitrary direction of the diffracted light.
  • 5. λ of Hg spectrumusing Grating - minimum deviation by spectrometer Grating equation : For normal incidence θi =0 and therefore ∆ =a sin θ. When ∆ =nλ, where n is an integer, all diffracted waves in the corresponding direction θn are in phase, and their amplitudes add up to give maximum intensity. Thus, we have the grating equation, which gives the positions of the intensity maximaas asin θn =nλ , n =0, ±1, ±2,. .
  • 6. λ of Hg spectrumusing Grating - minimum deviation by spectrometer Diffraction Grating:
  • 7. λ of Hg spectrumusing Grating - minimum deviation by spectrometer Aim : Todetermine the wavelengths of light emitted by amercuryvapour lampby using adiffraction grating Apparatus : Spectrometer, grating and holder, mercuryvapour lamp, magnifying lens, Spirit level
  • 8. λ of Hg spectrumusing Grating - minimumdeviation by spectrometer Procedure: 1. Setting the prismtable The prism table is made horizontal first with the help of a spirit-level by adjusting the leveling screws D, E and F To start with, the prism-table is rotated about its axis and adjusted in such a way that the parallel straight lines along with the two screws E and F are perpendicular to the axis joining the collimator and the telescope when they are aligned. A three way spirit level is kept on the prism tablewith its edgealongthe parallellines.
  • 9. λ of Hg spectrumusing Grating - minimumdeviation by spectrometer Procedure: 2. Setting up the Spectrometer Turn on the mercurylamp. Now, look through the eyepieceof the telescope and slide the eyepiecein and out until the cross-hairs comeinto sharp focus. Focusthe telescope at infinity by rotating focus knob. This is best accomplishedby focusing on a distant object(e.g.; out the window). Now, align the telescope directly opposite the collimator. View the slit through the telescope, rotate the telescope slightly if necessary, you should seesomelight if the slit is openpartially. Adjust the focus knob of collimator to makethe sharpimageof the slit. Do not changethe focus of the telescope. Finally, narrowdown the slit asmuchaspossibleand fine adjust the focus if necessary.
  • 10. λ of Hg spectrumusing Grating - minimumdeviation by spectrometer Procedure: 3. Normal incidence: Thetelescopeis brought in aline with the collimator and the direct imageof the slit is made to coincidewith the vertical crosswire. Thereadings of one vernier arenoted. Thevernier table is firmly clamped. Now, the telescope is rotated exactly through 90° and is fixed in this position. Thegrating is mounted vertically on the prismtable with its ruled surface facing the collimator. The vernier table is releasedand is slowly rotated till the reflected image coincideswith the vertical crosswire. Theleveling screwsareadjusted sothat the imageis at the centreof the field of view of the telescope.
  • 11. λ of Hg spectrumusing Grating - minimumdeviation by spectrometer Procedure: 3. Normal incidence: Theprism table is fixed and after making fine adjustments with the tangential screw, the readingsof the vernier arenoted. Now, the angle of incidenceis 45°. Thevernier table is then releasedand rotated exactly through 45° in the properdirection sothat the surface of the grating becomesnormal to the incident light. The vernier table is firmly clamped in this position. Thetelescope is then releasedand is brought to observethe direct image. .
  • 12. λ of Hg spectrumusing Grating - minimumdeviation by spectrometer Procedure: 3. Diffraction Pattern Onthe either side of the direct image,the diffraction spectra areseen.Thetelescope is turned slowly towards the left sothat the vertical crosswire coincideswith the violet lines of the first order.The readingsof the vernier aretaken. Thevertical crosswire is then madeto coincide with the other lines onthe left and the vernier readingsaretaken in eachcase. Thetelescope is then moved to the right and the readingof different lines is similarly taken.
  • 13. λ of Hg spectrumusing Grating - minimumdeviation by spectrometer Procedure: 3. Diffraction Pattern Thedifference between the readings on the left and right on the samevernier is determined for eachline. Themeanvalue of this difference gives 2θ-twice the angleof diffraction. Thus the angleof diffraction θ for eachspectral line is determined. Thewavelength of the greenline is 546.1 x10-9m. Thenumberof lines permeter(N) of the grating is calculated. Using this value of N, the wavelengths of the other prominent lines in this spectrum arecalculated.
  • 14. λ of Hg spectrumusing Grating - minimum deviation by spectrometer Formula: At normal incidence sin 𝜃 = 𝑁𝑛𝜆 N 𝜃 𝜆 Number of lines/mm in grating Angle of diffraction in degrees Wavelength in meters
  • 15. λ of Hg spectrumusing Grating - minimum deviation by spectrometer Tables: Tofind N
  • 16. λ of Hg spectrumusing Grating - minimum deviation by spectrometer Tables:
  • 17. λ of Hg spectrumusing Grating - minimum deviation by spectrometer
  • 18. λ of Hg spectrumusing Grating - minimum deviation by spectrometer Result : Thewavelength of prominentlines in the mercuryspectrum are Red orange------ yellow------- Green----- Blue ----- Violet