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Investigatory Project for Class 12 CBSE. The project is on the topic : Prism to calculate the refractive index of the prism and its minimum deviation angle.
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EXPERIMENT NO. :Object: To determine the dispersive power of the material of a prism with the help of a spectrometer. Apparatus: Spectrometer, glass prism, reading lens, a source of white light, eye piece, sprit level. Formula used: The
refractive
index
µ=
of
material
of
prism
A + δm 2 A sin 2
is
given
by
the
formula:
sin
(1)
where A is angle of prism and δm is the angle of minimum deviation for particular line of spectrum. The dispersive power (ω ) of the material of the a prism is given by
ω=
µ g − µr µy −1
Where , ω = dispersive power of the material of prism µ g = refractive index of green light µ r = refractive index of red light µ y = refractive index of yellow light. a) Adjustment of Spectrometer The following adjustments should be done: I) The optical axes of telescope and collimator should be perpendicular to the axis of rotation of the turn table and should meet at the same point. This adjustment is done by the manufacturer. II) Adjustment of the turn table: 1. The prism table is leveled with the help of three screws beneath the prism table. A spirit level is placed along the line joining the screws and the two screws are moved till the air bubble moves in the middle. Now place the spirit level along a line perpendicular to the previous line and adjust the third screw such that again the air bubble appears in the middle.
Here one thing should be remembered that first two screws should not be touched this time. The prism table is now leveled.
2. The second method which is generally used is optical leveling of the prism table. In this method the prism is placed on the prism table with its refracting edge at the centre of the prism table and one of its opaque surface perpendicular to the line joining the two leveling screws P and Q as shown in fig 1(a).
fig 1(a) 3. Now rotate the prism table in such a way that refracting edges AB and AC face towards the collimator and light falling on the prism is usually reflected from both the sides as in fig 1(b). The telescope is moved to the one side to receive the light reflected from the face AB and the leveling screws P and Q are adjusted to obtain image in the central field of view of the telescope. Again the telescope is moved to the other side to receive light reflected from face AC and remaining third screw R is adjusted till image becomes in central field of view of this telescope. The prism table is now leveled. III) Schuster’s method for focusing the telescope and collimator: a) First of all prism is placed on the prism table and then adjusted for minimum deviation position. The spectrum is now seen through the telescope. (Note: The turn table is rotated such that the light from the collimator may fall on the face AB and emerge through the face AC so that the spectrum is visible in the field of view of the telescope. Now, if the prism table is slightly rotated in the either direction till the spectrum is obtained. The spectrum during the rotation of the table moves in one direction and it begins to retrace the path from a certain position when the rotation is still continued in the same direction. At this position, the rays suffer minimum deviation.) b) The prism table is rotated slightly away from this position towards the collimator and spectrum is viewed focusing collimator on the spectrum.
c) Again rotate the prism table on the other side of minimum deviation position i.e. towards the telescope and focus telescope for best image of the spectrum. d) The process of focusing the collimator and telescope is continued till the slight rotation of prism table does not make the image to go out of focus. This means that both the collimator and the telescope are now individually set for parallel rays.
Procedure: A. Measurement of the angle of prism (A) I. After the above adjustments, slit is made narrow .The prism is placed with its refracting edge at the centre of the turn table in such a way such that a part of light from collimator is incident on the face AB while the rest is incident on the face AC as in fig b. II. The telescope is turned till we get image of the slit as reflected from the face AB. The telescope is clamped and the image is coincided with the intersection of cross wires. III. Without moving the prism on the table, telescope is turned to receive light from other reflecting surface and same procedure is repeated. IV. The difference between the readings in the two positions is equal to twice the angle of prism.
B. Measurement of the angle of minimum deviation( δm ) V. The turn table is rotated such that the light from the collimator may fall on the face AB and emerge through the face AC so that the spectrum is visible in the field of view of the telescope. Now, if the prism table is slightly rotated in the either direction the angle of incidence on the face AB changes. The refracted image of slit (spectrum) is obtained. The spectrum during the rotation of the table moves in one direction and it begins to retrace the path from a certain position when the rotation is still continued in the same direction. At this position, the rays suffer minimum deviation. The cross-wires are coincided with any spectral line, say red. The reading of both the verniers is taken.
VI. The table is now rotated on the other side so that the rays are now incident on the face AC and emerge through AB and the procedure is repeated as in (I).The difference between the readings on the either side of the direct ray gives double the angle of minimum deviation.
VII. Similar observations for the angle of minimum deviation are also recorded for the other spectral lines of two other colors.(say green and violet) Observations:
[A]Least count of spectrometer=
degrees
[B] Readings for determination of A:
S No
Vernier Position of the image Reflected from AB
.
Reflected from AC
M.S
Vernier
Total
M.S
Vernier
Total
reading
Reading
reading
reading(i
Reading
reading(Y)
(in
(in
(X)
n
(in
(in
degrees)
degrees)
degrees)
degrees)
degrees)
degrees)
(in
V1 1 V2 2
V1 V2
3
V1 V2
Mean 2A= [C] Readings for determination of δm
Color of
Vernier Readings for minimum deviation Light incident on face AB Light incident on face AC
2A=(X-Y) (in degrees)
the
M.S
Vernier
Total
M.S
Vernier
Total
2 δm =U-V
line
reading
Readin
reading
reading
Reading
reading
(in
(in
g
(U)
(in
(in
(V)
degrees)
degrees)
(in
(in
degrees)
degrees)
(in
degrees)
degrees)
degrees)
V1 Red V2 Yello w
green
V1 V2 V1 V2
Calculations: Mean value of A= Mean value of δm a) For red line = b) For yellow line =
c) For green line = Therefore:
µ=
A + δm 2 A sin 2
sin
And so the dispersive power (ω ) of the material of the a prism is given by ω=
µ g − µr µy −1
Result: The refractive index of material of prism:
a) for red line ( µr ) =
b) for yellow line ( µy ) = c) for green line ( µv ) = d) And so the dispersive power (ω ) of the material of the a prism is given by ω=
µ g − µr µy −1
Precautions: 1) Both the telescope and the collimator should be fixed for parallel rays. 2) The eye-piece should be focused on the cross-wires. 3) While taking the observations, the slit should be made narrow.
4) Both the verniers should be read which eliminates the error due to non-coincidence of the centre of graduated circle with the axis of rotation of the table. Sources of error: 1. The spectrometer is not properly adjusted. 2. Error may be due to parallax. 3. If the reading is not taken overhead the spectrometer. 4. Reading may not be taken taking care of precautions. Maximum Probable error: Taking log on both sides of equation (1):
A + δm A ) − log(sin ) 2 2 Differentiating both sides with A and δm as variables maximum probable error in µ can log µ = log(sin
be calculated which is dµ /µ . Using maximum probable error of µ calculate the maximum probable error of ω .
