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Experiment-2 :: To measure the refractive index of the prism for different wavelengths and then draw dispersive curve.

Equipment: Spectrometer, Mercury lamp, Prism

Theory: A spectrometer is used for this purpose. A Hg lamp, preferably low pressure, provides the illumination. The refractive index is obtained from the relation:

Exp2

where A is the angle of the prism and δm is the angle of minimum deviation for a particular wavelength. Usually a 600 prism is used for this experiment. At minimum deviation, the ray of a particular wavelength propagates parallel to the base. Alternately angle of incidence and angle of emergence are equal.  Since single ray is mathematical realization, a collimated beam (parallel beam) is incident on the prism face and the emergent beam is also collimated.
From the figure it is seen that the dispersion takes place at the first surface of the prism and refraction alone takes place at the second surface. The angle of deviation δ is related to the angle of incidence as :
Eqations

It can be shown that the angle of deviation is minimum when a = b.
This experiment requires the measurement of angle (A) of the prism and the angle of minimum deviation for each colour.

Procedure: In order to get the collimated illumination incident on the prism face and to receive the collimated emergent beam, spectrometer is to be set up. Following steps are needed:

SETTING UP SPECTROMETER

Step 1: Focus the eye-piece on the crosswire or graticule by moving the eye-piece in and out in the tube.

Step 2: Observe a distant object (located at least 5 meters from the telescope) and using rack and pinion on telescope, focus the object on crosswire.The telescope is now set to receive a parallel beam.

Step 3: Place the spectrometer near the lamp with slit very close to it. Align the telescope in line with the collimator and see the image of the slit. By using a rack and pinion arrangement on the collimator, make a sharp image of the slit on the crosswire. Adjust the slit width to be such that its image is very fine but quite bright. Slit image must be slightly bigger than the diameter of the crosswire.


Step 4: Take the readings of collimator and telescope on both the verniers. As a check the difference between the corresponding collimator and telescope readings must be 180°. The collimator is fastened and the telescope is free to move.

Step 5: Place the prism on the turn table such that the refracting edge is towards the collimator. Observe the image reflected from the sides of the prism and adjust the turntable such that the images appear at the same height on both sides.

Measurement of angle of the prism:
A A Step 6: Observe the slit image as seen by reflection from one of the surfaces, bring the crosswire on the slit image and take the readings on the verniers.

Step 7: Observe the slit image on reflection from the other surface of the prism and bring it on the crosswire. Take the readings on both the verniers.

Step 8: The difference between the readings of the corresponding verniers is equal to 2A.
Prism Angle calculation-Collimator Position-1 Prism Angle calculation-Collimator Position-2
 
Observation of spectrum Step 9: Place the prism as shown on the turn table and observe the spectrum. Spectrum may be seen when the telescope is properly brought to receive it.
Step 10: Turn the turntable. The spectrum will now move and as the turntable is rotated in the same direction the spectrum would retrace the direction. Fix the telescope when this position is reached. Using fine motion bring the crosswire on a particular spectral line. Check again by turning the turntable whether this is the position for this spectral line when it just changes its direction. Take the reading on both the verniers.
Step 11: Repeat this for other spectral lines. Remember that whole spectrum is not at a minimum deviation when the spectrum changes direction on rotating the turntable in the same direction. Therefore find the position of minimum deviation for each spectral line.
Step 12: Bring the telescope in line with the collimator. Now you should see the image of the slit in undispersed light. Adjust the telescope with fine motion screws such that the slit image is on the crosswire. Take readings of both the verniers.
Step 13: Difference between the readings of the corresponding verniers will now give the value of the angle of minimum deviation for that colour.
Note: Since we are making measurement using circular scale (0 to 3600), care must be exercised when the readings are subtracted.
Step 14: Calculate the refractive index for different spectral lines (colours) and then draw the graph between refractive index and wavelength. This is the dispersion curve.

Observations:
Measurement of the angle of the prism:

S.No.

Reflection from left surface

Reflection from right surface

A=(Vr1-Vl1)/2

 

Vernier Vl1

Vernier Vl2

Vernier Vr1

Vernier Vr2

A=(Vr2-Vl2)/2

1

 

 

 

 

 

2

 

 

 

 

 

3

 

 

 

 

 

Average value of the prism angle=________degrees
Measurement of the angle of minimum deviation:_______
Telescope position-aligned in line with collimator: Vt1 and Vt2

S.No.

Wavelength

Reading at minimum deviation position

δ=(Vm1-Vt1)

m

 

 

Vernier Vm1

Vernier Vm2

δ=(Vm2-Vt2)

 

1

 

 

 

 

 

2

5461 (Green)

 

 

 

 

3

 

 

 

 

 

4

4358 (blue)

 

 

 

 

5

 

 

 

 

 

6

 

 

 

 

 

Questions:

  • What causes the formation of spectrum? And where is it formed?
  • What is the roll of second surface of the prism?
  • Derive the equation (2) and prove that at minimum deviation a=e.

DISPERSION CURVE
 
 
 
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