1

Physics Lab Manual

For

Diploma in Engineering

Ist Year

2

PHYSICS LAB

LIST OF EXPERIMENTS

1. To measure the thickness of the given glass plate using Screw Gauge.

2. To measure the length and diameter of the given solid cylinder using Vernier calipers.

3. To measure the thickness of the given glass plate using Spherometer.

4. To verify the Ohm's Law for a given conductor and to determine the resistance of a given

conductor by using the I-V characteristics.

5. To determine the value of 'g' by using a Simple Pendulum.

6. To determine the value of 'g' by using a Kater’s Pendulum.

7. To Study the variation of magnetic field with increasing distance from centre of a

Helmholtz coil Tangent Galvanometer.

8. To compare the E.M.F. of two primary cells by using a Potentiometer.

9. To determine the unknown resistance, resistivity and conductivity of a given wire by using

Meter Bridge.

10. To determine the angle of deviation and Refractive Index of a given Prism by

Spectrometer.

3

EXPERIMENT 1 Screw Gauge

OBJECTIVE

To measure diameter of a given wire using a screw gauge and find its volume.

APPARATUS

Screw gauge, wire.

THEORY

If with the wire between plane faces A and B, the edge of the cap lies ahead of

Nth division of linear scale.

Then, linear scale reading (L.S.R.) = N

If nth division of circular scale lies over reference line.

Then, circular scale reading (C.S.R.) =nx (L.C.) (L.C. is least count of screw gauge)

Total reading (T.R) =L.S.R. +C.S.R. =N+nx (L.C.).

DIAGRAM

PROCEDURE

1. Find the value of one linear scale division (L.S.D.).

2. Determine the pitch and the least count of the screw gauge and record it stepwise.

3. Bring the plane face B in contact with plane face A and find the zero error. Do it three times and

record them. If there is no zero error, then record 'zero error nil'.

4. Move the face B away from face A. Place the wire lengthwise over face A and move. The face B

towards face A using the ratchet head R. Stop when R turns (slips) without moving the screw.

5. Note the number of divisions of the linear scale visible and uncovered by the edge of the cap. The

reading (N) is called linear scale reading (L.S.R.).

6. Note the number (n) of the division of the circular scale lying over reference line.

7. Repeat steps 5 and 6 after rotating the wire by 90° for measuring diameter in a perpendicular

direction.

8. Repeat steps 4, 5, 6 and 7 for five different positions separated equally throughout the length of

the wire. Record the observations in each set in a tabular form.

9. Find total reading and apply zero correction in each case.

10. Take mean of different values of diameter.

4

11. Measure the length of the wire by stretching it along a half metre scale. Keeping one end of wire

at a known mark, note the position of other end. Difference in position of the two ends of the wire

gives the length of the wire. Do it three times and record them.

OBSERVATIONS

1. Determination of Least Count of the Screw Gauge

1L.S.D. = 1mm

Number of full rotations given to screw= 4

Distance moved by the screw = 4 mm

Hence, pitch=4mm/4=1mm

Number of divisions on circular scale = 100

Hence, least count = 1mm/100= 0.01 mm= 0.001 cm.

2. Zero Error.

Zero error (e) = mm

Zero correction (c) = .......mm.

To measure the diameter

CALCULATIONS

Mean diameter =........mm

RESULT

The diameter of the given wire =.............

PRECAUTIONS

1. To avoid undue pressure; the screw should always be rotated by ratchet R and not by cap K.

2. The screw should move freely without friction.

3. The zero correction, with proper sign should be noted very carefully and added algebraically.

4. For same set of observations, the screw should be moved in the same direction to avoid back-

Lash error of the screw.

5. At each place, the diameter of the wire should be measured in two perpendicular directions and

then the mean of the two be taken.

6. Readings should be taken at least for five different places equally spaced along the whole length

of the wire.

7. Error due to parallax should be avoided.

SOURCES OF ERROR

1. The screw may have friction.

2. The screw gauge may have backlash error.

3. Circular scale divisions may not be of equal size.

4. The wire may not be uniform.

5

EXPERIMENT 2 Vernier Callipers

OBJECTIVE:

Use of Vernier Calipers to

(i) Measure diameter of a small spherical/cylindrical body,

(ii) Measure the dimensions of a given regular body of known mass and hence to determine its den-

sity; and

(iii) Measure the internal diameter and depth of a given cylindrical object like beak-

er/glass/calorimeter and hence to calculate its volume.

APPARATUS AND MATERIAL REQUIRED Vernier Callipers, Spherical body, such as a pend l m bob or a glass marble, rectangular block of known mass and cylindrical object like a beaker/glass/calorimeter

DESCRIPTION OF THE MEASURING DEVICE

1. A Vernier Calliper has two scales–one main scale and a Vernier scale, which slides along the main scale.

The main scale and Vernier scale are divided into small divisions though of different magnitudes. The

main scale is graduated in cm and mm. It has two fixed jaws, A and C, projected at right angles to the

scale. The sliding Vernier scale has jaws (B, D) projecting at right angles to it and also the main scale and

a metallic strip (N). The zero of main scale and Vernier scale coincide when he jaws are made to

touch each her. The jaws and metallic strip are designed to measure the distance/ diameter of objects.

Knob P is used to slide the vernier scale on the main scale. Screw S is used to fix the Vernier Scale at a

desired position. 2. The least count of a common scale is 1mm. It is difficult to further subdivide it to improve the least count

of the scale. A vernier scale enables this to be achieved.

PRINCIPLE: The difference in the magnitude of one main scale division (M.S.D.) and one vernier scale division (V.S.D.) is

called the least count of the instrument, as it is the smallest distance that can be measured using the instrument.

6

n V.S.D. = (n – 1) M.S.D.

OBSERVATIONS: (i) Least count of Vernier Callipers (Vernier Constant)

1 main scale division (MSD) = 1 mm = 0.1 cm

Number of vernier scale divisions, N = 10

10 vernier scale divisions = 9 main scale divisions

1 vernier scale division = 0.9 main scale division

Vernier constant = 1 main scale division – 1 vernier scale division

= (1– 0.9) main scale divisions

= 0.1 main scale division

Vernier constant (VC) = 0.1 mm = 0.01 cm

Alternatively

(ii) Zero error and its correction

When the jaws A and B touch each other, the zero of the Vernier should

coincide with the zero of the main scale. If it is not so, the instrument is said to

possess zero error (e). Zero error may be positive or negative, depending upon

whether the zero of vernier scale lies to the right or to the left of the zero of the

main scale. This is shown by the Fig. (ii) and (iii). In this situation, a correction

is required to the observed readings.

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Zero error (i) no zero error (ii) positive zero error (iii) negative zero error

(iii) Positive zero error

Fig E 1.2 (ii) shows an example of positive zero error. From the figure, one can

see that when both jaws are touch ng each other, zero of the vernier scale is

shifted to the right of zero of the main scale (This might have happened due to

manufacturing defect or due to rough handling). This situation makes it o

various that while taking measurements, the reading taken will be more than the

actual reading. Hence, a correction needs to be applied which is proportional to

the right shift of zero of vernier scale.

In ideal case, zero of vernier scale should coincide with zero of main scale.

But in Fig. (ii), 5th vernier division is coinciding with a main scale reading.

∴ Zero Error = + 5 × Least Count = + 0.05 cm

Hence, the zero error is positive in this case. For any measurements done, the zero

error (+ 0.05 cm in this example) should be ‘subtracted’ from the o served reading.

Table E 1.1 (a): Measuring the diameter of a small spherical/ cylindrical body

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Table E 1.1 (b) : Measuring dimensions of a given regular body

Table E 1.1 (c): Measuring internal diameter and depth of a given beaker/

calorimeter/ cylindrical glass

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CALCULATIONS

10

RESULTS:

PRECAUTIONS

11

SOURCES OF ERROR Any measurement made using Vernier Callipers likely to be incorrect if-

(i) the zero error in the instrument placed is not accounted for; and

(ii) the Vernier Callipers is not in a proper position with respect to the

body, avoiding gaps or undue pressure or both.

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EXPERIMENT No- 3

Spherometer

OBJECTIVE: To find the focal length of a convex mirror using a spherometer

EQUIPMENT REQUIRED: - a spherometer, a plane glass plate, a convex mirror and a metre

scale.

THEORY:-

Radius of curvature of a spherical surface can be determined by using the formula,

Diagram of Spherometer

Figure: Spherometer

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OBSERVATIONS AND CALCULATIONS

CALCULATIONS

14

PROCEDURE:

RESULTS: Focal length of the convex mirror, f=………………… cm

PRECAUTIONS:

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EXPERIMENT No- 4

Verification of Ohm’s law.

OBJECTIVE: Verification of Ohm’s law.

EQUIPMENT REQUIRED: - Accumulator or battery eliminator, ammeter, voltmeter, rheostat,

Coil, connecting wires and key (if necessary).

THEORY:-

Ohm's Law deals with the relationship between voltage and current in an ideal conductor.

This relationship states that:

The potential difference (voltage) across an ideal conductor is proportional to the current through it.

The constant of proportionality is called the "resistance", R. Ohm's Law is given by:

V = I R Where V is the potential difference between two points which include a resistance R.

I is the current flowing through the resistance.

Or

Ohm’s law states that the current through a conductor between two points is directly proportional to

the voltage across the two points, and inversely proportional to the resistance between them. V, I,

and R, the parameters of Ohm's law.

I = V / R

Ohm's law is among the most fundamental relationships in electrical engineering. It relates the cur-

rent, voltage, and resistance for a circuit element so that if we know two of the three quantities we

can determine the third. Thus, if we measure the current flowing in a resistor of known value, we

can deduce the voltage across the resistance according to V = IR. Similarly, if we measure the volt-

age across a resistor and the current through it, we calculate the resistance of the element to be

R = V/I.

Not only does this reduce the number of measurements that must be made, it also provides a way to

check the results of several different measurement methods.

CIRCUIT DIAGRAM:-

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PROCEDURE:-

1) Connect the battery eliminator, ammeter, the given coil, rheostat and key (if necessary) in

series.

2) The voltmeter is connected in parallel connection across the given coil. The circuit is closed.

3) Now the rheostat is adjusted so that a constant current flows through the coil. Note down the

ammeter reading I and the corresponding potential difference across the coil in the voltmeter

as V.

4) Use the formula to calculate the resistance of the coil.

5) The experiment is repeated for different values of current and the corresponding potential

difference is noted. Calculate the value in each trial.

6) These values will be found to be a constant. Thus verifying Ohm's law.

OBSERVATION TABLE:-

RESULT:-

By observing the observation table, it is proved that the ratio of potential difference and current is

constant. Thus, potential difference at the ends of the conductor is directly proportional to the cur-

rent flowing through it. Thus, ohm’s law is verified by this experiment.

PRECAUTIONS: -

1) All the connection should be tight.

2) Ammeter is always connected in series in the circuit while voltmeter is parallel to the conductor.

3) The electrical current should not flow the circuit for long time, otherwise its temperature will in-

crease and the result will be affected.

4) Maximum reading of voltmeter should be greater than the electromotive force of the cell.

5) It should be care that the values of the components of the circuit is does not exceed to their

ratings (maximum value).

6) Before the circuit connection it should be check out working condition of all the components.

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EXPERIMENT 5

Measurement of g: Use of a simple pendulum

OBJECTIVE: To measure the acceleration due to gravity using a simple pendulum.

INTRODUCTION:

Many things in nature wiggle in a periodic fashion. That is, they vibrate. One such example is a simple pendulum. If we suspend a mass at the end of a piece of string, we have a simple pendulum. Here, the to and fro motion represents a periodic motion used in times past to control the motion of grandfather and cuckoo clocks. Such oscillatory motion is called simple harmonic motion. It was Galileo who first observed that the time a pendulum takes to swing back and forth through small distances depends only on the length of the pendulum The time of this to and fro motion, called the period , does not depend on the mass of the pendulum or on the size of the arc through which it swings. Another factor involved in the

period of motion is, the acceleration due to gravity (g), which on the earth is 9.8 m/s2. It

follows then that a long pendulum has a greater period than a shorter pendulum.

PROCEDURE:

The period T of a simple pendulum (measured in seconds) is given by the formula:

T=2 π √ (L/g) (1)

T = time for 30 oscillations (2)

30 oscillations

using equation (1) to solve for “g”, L is the length of the pendulum (measured in meters)

and g is the acceleration due to gravity (measured in meters/sec2 ). Now with a bit of

algebraic rearranging, we may solve Eq. (1) for the acceleration due to gravity g. (You should derive this result on your own).

g = 4π²L/T2 (3)

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1. Measure the length of the pendulum to the middle of the pendulum bob.

Record the length of the pendulum in the table below.

2. With the help of a lab partner, set the pendulum in motion until it

completes 30 to and fro oscillations, taking care to record this time. Then the period

T for one oscillation is just the number recorded divided by 30 using (eq. 2).

3. You will make a total of eight measurements for g using two different

masses at four different values for the length L.

Note: π = 3.14, 4 π² = 39.44

L (meters) mass Time for 30 oscillations Period T (seconds) T² g = 39.44L/T2

Average value of g = __________ QUESTIONS:

1) From your data what effect does changing the mass have on the

period (for a given value of the length L)?

2) What role, if any, does air resistance have on your results?

Explain your reasoning.

3) Would you conclude that Galileo was correct in his observation

that the period of a simple pendulum depends only on the length of the

pendulum?

4) On the moon, the acceleration due to gravity is one-sixth that of earth.

That is

gmoon = gearth /6 = (9.8 m/s2)/6 = 1.63 m/s

2.

What effect, if any, would this have on the period of a pendulum of length L?

How would the period of this pendulum differ from an equivalent one on earth?

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EXPERIMENT 6 Measurement of g: Use of a Kater’s Pendulum

OBJECT:-|To determine the value of acceleration due to gravity with Kater’s pendulum.

APPARATUS:-Kater’s pendulum, a stop watch and a meter rod.

FORMULA:-

The following formula is used for the determination of acceleration due to gravity ‘g’:

------------- (1)

Here, T1: time periods of the oscillating pendulum from knife-edge K1

T2: time periods of the oscillating pendulum from knife-edge K2

l1: distances between knife-edges K1 and CG of the pendulum

l2: distances between knife-edges K2 and CG of the pendulum

When T1and T2 are very close to each other (difference less than 1 percent), the above expression

becomes as:

----------- (2)

PROCEDURE:

1. Fix the weights as shown in the figure.

2. Make sure that the distances from big masses to ends and big masses to knife edges should

be symmetrical.

3. Balance the pendulum on a sharp wedge such that the smaller weights are at symmetrical

distance from CG. Now mark the position of its centre of gravity and measure the distance

of the knife-edges K1and K2 CG. This will give you the values of l1 & l2 .

4. Suspend the pendulum with the knife-edge K1 and set it to oscillate with small amplitude.

Note the times for 15, 20 and 25 oscillations respectively.

5. Now suspend the pendulum with the knife-edge K2 and set it to oscillate with small ampli-

tude. Note the times for 15, 20 and 25 oscillations respectively.

6. The oscillations should be seen with the help of a telescope for accuracy.

20

OBSERVATION:

1. Least count of stop watch =........sec

2. Distance between K1and CG (l1) =........cm

3. Distance between K2 and CG (l2) =........cm

4. Table for time period T1 (oscillation about K1):

5. Table for time period T2 (oscillation about k2) :

CALCULATION:

Using equation (1) or (2) {depending on value of T1 and T2} calculate the value

of g.

RESULT:

The Acceleration due to gravity g = -------------- m/s2.

Standard value of g = 9.8 m/s2

PERCENTAGE ERROR: (∆g /g) x100% PRECAUTIONS: 1. The two knife-edges should be parallel to each other.

2. The amplitude of vibration should be small so that the motion of the pendulum satisfies the con-

dition of simple harmonic motion.

3. To avoid any irregularity of motion the time period should be noted after the pendulum has made

a few oscillation.

4. To avoid friction there should be glass surface on rigid support.

21

EXPERIMENT 7 Helmholtz Galvanometer

AIM - To study the variation of magnetic field with distance along the axis of Helmholtz galva-

nometer and to estimate the radius of the coil.

APPARATUS - Helmholtz galvanometer, magnetometer compass box, ammeter (measure mA),

battery eliminator, rheostat, commutator, plug key, connecting wires.

THEORY- The term Helmholtz coils refers to a device for producing a region of nearly uniform

magnetic field. It is named in honor of German physicist Hermann von Helmholtz. It consists of

two identical circular magnetic coils that are placed symmetrically parallel to each other and on a

common axis, z- axis. The rings have radius r and they are separated by a distance equal to or slight-

ly larger than r. Each coil carries an equal electrical current flowing in same direction.

Helmholtz coils

The first step to calculate the field of a pair of Helmholtz coil is to calculate magnetic field intensity

F produced by each ring.

If a current (I) is allowed to flow through a wire of length ( l ), and the wire is bent into an arc of ra-

dius r, then the magnetic field intensity (F) at center of the arc is

0

24

IlF

r

(1)

Where 0 = permeability of free space (8.854 x 10-12 F/m) For a circular coil of n turns we substitute l=2rn in equation (1)

0

2

InF

r

(2)

Now, substituting the value of 0 in equation (2)

The magnetic field produced by each ring is given by

7

2

10

nIF

r

(3) The magnetic field at any point on axis at a distance (x) from centre of coil is

2

3

7 2 2 2

2

10 ( )

nIrF

x r

(4)

22

The rate of variation of magnetic field.

Figure2. Magnetic field generated by a coil with radius (r) =1m.

Figure3. Magnetic field generated by a pair of Helmholtz coils

Therefore, 5

2 2 2 2

5 722 2 2 2 2 22 2

2

3 [(2 )( ) ]

[ 6 ( ) 5 ( ) ]

dFx nir x r

dx

d Fnir x r x x r

dx

From which, 2rx

, if 0

2

2

dx

Fd

or

dx

dF

constant.

Thus at point 2rx

from centre of coil,

dF

dx

constant

We observe that in figure3, the rate of increase of field due to one coil at midpoint between the coils is equal

to the rate of decrease of field due to the other at the same point. Therefore if one moves away along the axis

from the midpoint, any diminution in the intensity of the field due to one coil is compensated by the increase

in the field due to the other so that the field between the coils is practically uniform.

The coil is placed in the magnetic meridian, the magnetic field due to the current I flowing in the coil is

perpendicular to H (Horizontal component of earth’s magnetic field). Thus the magnetic needle is acted upon

by two uniform magnetic fields F and H at right angles to each other.

The magnetic needle will make an angle with H in the equilibrium position.

According to tangent law:

F = H tan Therefore

2

3

227

2

)(10

2tan

rx

nIr

(5)

23

Note: tan α I

tan α 1 r3

MAGNETOMETER: The magnetic compass box used in this experiment is called Magnetometer. The red

point in the magnetometer corresponds to North direction (Red is analogous to positive terminal of electrical

circuit.). Thus in absence of magnetic field the needles are in east west direction and while performing the

experiment in order to avoid to the Earth’s horizontal magnetic field the bench of the Helmholtz

galvanometer should be kept in east-west direction.

PROCEDURE-

1. The Helmholtz coils should be parallel to themselves and perpendicular to the bench and at a dis-

tance equal to 2r

on either side from centre of the bench. 2. Magnet compass box is kept at kept at the centre of the sliding bench, such that magnetic needle is

at the centre of the coils.

3. The bench of the Helmholtz galvanometer should be kept in east-west direction

4. Base of the coil is levelled with the help of spirit level and levelling screws.

5. Connections are made as shown in figure using say 50 turns of the coil and taking care that out of the

four terminals provided on the commutator K any two diagonally opposite terminals are joined to the

galvanometer and the other two to the battery through rheostat.

Figure. Circuit diagram

6. Adjust the current in the coil with the help of rheostat such that the deflection in the magnetic needle

is of the order of 45 at centre of bench for both direct and reverse current. 7. Now move the compass box through 2 cm and note the deflection in east and west direction of mag-

netometer for direct and reverse current respectively.

8. Continue to take readings till +/-15 deflection is obtained in the compass box with respect to 45. 9. Repeat the procedure for other side.

10. Calculate mean and find tan according to the observation table.

11. Plot a graph taking x on x-axis and tan on y-axis respectively for each side. Mark the points of in-

flection on the curve. The distance between the two points will be the diameter of the coil.

12. The circumference of the coil can be measured by a thread and its radius can be calculated to verify

the value obtained from the graph

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OBSERVATIONS-

S.No.

Position of the

needle on one of

the scale.

(Distance of

Compass box

from center of

coil)

x (cm)

Deflection in the needle when it is on one side of bench

Current one way Current reversed

Mean

(degree)

Tan

1

East

end of

needle

2

West

end of

needle

3

East

end of

needle

4

West

end of

needle

1. 0

2. 2

3. 4

4. 6

5. 8

6. 10

7. 12

8. 14

9. 16

10. 18

11. 20

12. 22

13. 24

14. 26

15. 28

16. 30

25

S.No.

Position of the

needle on one of

the scale.

(Distance of

Compass box

from center of

coil)

x (cm.)

DeDeflection in the needle when it is on other side of bench

Current one

way Current reversed

Mean

degree

Tan

1

East

end of

needle

2

West

end of

needle

3

East

end of

needle

4

West

end of

needle

1. 0

2. 2

3. 4

4. 6

5. 8

6. 10

7. 12

8. 14

9. 16

10. 18

11. 20

12. 22

13. 24

14. 26

15. 28

16. 30

26

GRAPH:

west east

CALCULATION-

Circumference of the coil as obtained by a thread and meter scale = …..cm.

Radius of the coil, as obtained from the graph = distance between the points A and B.

Radius of the coil, as obtained from measurement = 2

nceCircumfereIts

(6)

MAXIMUM PROBABLE ERROR:- This is obtained by taking logarithmic differentiation of equation (6)

RESULT: - 1. The variation in the magnetic field with distance, along the axis of the given coil is as shown

in the graph.

2. Radius of the coil = __________cm. as obtained from the graph and__________cm.

as obtained from measurement.

PRECAUTIONS-

1. Connections should be clean and tight.

2. Circuit should be properly connected and checked before turning it “ON”. No. of turns should be

equal in both coils.

3. Plug key should be used in circuit and it should not be closed while making connections or taking

reading.

4. The coil should be adjusted properly in the magnetic meridian.

5. The apparatus should be at considerable distance from current carrying conductors and magnetic ma-

terials.

6. The positive marked terminal of the ammeter should be always connected to positive terminal of bat-

tery.

7. While taking readings there can be error due to parallax which should be avoided.

8. Readings at both ends of the pointer should be taken.

SOURCES OF ERROR-

1. Connections might not be tight.

2. Magnetic needle might not be pivoted at center.

3. Galvanometer coil might not be exactly in magnetic meridian.

27

EXPERIMENT 8 Comparison of E.M.F of Two Primary Cells by Potentiometer

OBJECTIVE:

28

29

30

31

EXPERIMENT 9 Meter Bridge

OBJECTIVE: To find the resistance of a given wire using a metre bridge and hence determine the

specific resistance of its materials.

APPARATUS: A meter bridge, galvanometer, one way key, a resistance box, a battery jockey, un-

known resistance wire about 1 meter long, screw gauge and connecting wires.

THEORY:

A meter bridge is the practical application of Wheatstone bridge arrangement as shown in figure

below. The four resistances are connected to each other as shown and if the bridge is in balanced

state, i.e., there is no deflection in the galvanometer (G),

P/Q = R/S

Resistance of the wire R

X

l

lRX

Specific resistance of the material of the wire l

Xr 2

\

Where R is known resistance

Rl is the balancing length of R

Xl is the balancing length of X

r is the radius of the wire

l is the length of the wire

Circuit diagram – Before interchanging

32

Circuit diagram – After interchanging

PROCEDURE

The connections are made as in the circuit diagram. The jockey J is pressed near the ends A

and C and if the deflections in the galvanometer are in the opposite directions, then the circuit is

correct. Now the jockey is moved over the wire and its position J is found when there is no

deflection in the galvanometer. The balancing length AJ = ℓR1 is measured. JC =ℓX1 is found out

as (100 - ℓR1).

The experiment is repeated four more times by increasing the value of R in steps of 1 ohm.

Then the resistance box R and coil X are interchanged in the gaps G1 and G2. For the same

values of R as in the previous part of the experiment the balancing length AJ =ℓX2 are measured.

The balancing length JC =ℓR2 are found out as (100- ℓX2). The values of ℓX and ℓR are calculated

from

2

21 XXX

2

21 RRR

The resistance of the coil is found by substituting in the formula

The length (ℓ) of the coil is measured using scale and radius(r) of the coil is measured using screw

gauge. The specific resistance of the coil is calculated using the formula

l

Xr 2

OBSERVATION

(i) To determine the resistance of the given coil

S.N

o

R

(ohm)

Balancing

length before

interchanging

Balancing

length after

interchanging

Mean R

X

l

lRX

(ohm)

1x (c

m)

1R (c

m)

2X (c

m)

2R (c

m) 2

2X1XX

(cm) 2

2R1RR

(cm)

1 1

33

2 2

3 3

(ii) To determine the radius of the coil

LC = 0.01 10–3m

ZERO ERROR = ZERO CORRECTION =

S.No PSR HSC HSR CR = PSR+HSRL.C

1

2

3

4

Diameter 2r

r

CALCULATION:

= =

= =

= =

= =

Calculation for X

=

=

=

34

=

=

Mean X = =

Calculation for :

=

RESULT:

Resistance of the wire X =

Specific resistance of the material of the wire = m

PRECAUTIONS:

1. All the connections should be correct and tight.

2. Only small amount of resistance will be applied through the resistance box.

3. The Jockey should be sliding over the entire wire steadily and not be connected for long.

4. Switch off the power supply when experiment is over.

35

EXPERIMENT 10 Prism Spectrometer

1 AIM OF EXPERIMENT

To calculate the Refractive Index of the Prism for various wavelengths of the Mercury Spectrum

and then plot a Dispersion and Calibration Curves using a Prism Spectrometer.

2 APPARATUS REQUIRED

a) Mercury lamp (as source of white light)

b) Spectrometer

c) Prism

d) Spirit level

3 THEORY OF EXPERIMENT

The spectrometer is an instrument for analyzing the spectra of radiations. The glass-prism spec-

trometer is suitable for measuring ray deviations and refractive indices. Sometimes a diffraction

grating is used in place of the prism for studying optical spectra. A prism refracts the light into a

single spectrum, whereas the diffraction grating divides the available light into several spectra. Be-

cause of this, slit images formed using a prism are generally brighter than those formed using a grat-

ing. Spectral lines that are too dim to be seen with a grating can often be seen using a prism.

Unfortunately, the increased brightness of the spectral lines is offset by a decreased resolution, since

the prism doesn’t separate the different lines as effectively as the grating. However, the brighter

lines allow a narrow slit width to be used, which partially compensates for the reduced resolution.

With a prism, the angle of refraction is not directly proportional to the wavelength of the light.

Therefore, to measure wavelengths using a prism, a calibration graph of the angle of deviation

versus wavelength must be constructed using a light source with a known spectrum.

The wavelength of unknown spectral lines can then be interpolated from the graph.

Once a calibration graph is created for the prism, future wavelength determinations are valid only if

they are made with the prism aligned precisely as it was when the graph was produced. To ensure

that this alignment can be reproduced, all measurements are made with the prism aligned so that the

light is refracted at the angle of minimum deviation.

The light to be examined is rendered parallel by a collimator consisting of a tube with a slit of

adjustable width at one end and a convex lens at the other. The collimator has to be focused by

adjusting the position of the slit until it is at the focal point of the lens. The parallel beam of light

from the collimator passes through a glass prism standing on a prism-table which can be rotated,

raised or lowered, and levelled. The prism deviates the component colors of the emitted light by

different amounts and the spectrum so produced is examined by means of a telescope, which is

mounted on a rotating arm and moves over a divided angular scale.

The theory of the prism spectrometer indicates that a spectrum of maximum definition is obtained

when the angular deviation of a light ray passing through the prism is a minimum. Under such

conditions it can be shown that the ray passes through the prism symmetrically. For a given wave-

length of light traversing a given prism, there is a characteristic angle of incidence for which the

angle of deviation is a minimum. This angle depends only on the index of refraction of the prism

and the angle between the two sides of the prism traversed by the light. The relationship between

these variables is given by the equation:

36

Where n is the index of refraction of the prism and δm is the angle between the sides of the prism

traversed by the light and is the angle of minimum deviation. Since n varies with wavelength, the

angle of minimum deviation also varies, but it is constant for any particular wavelength.

The telescope can also be locked or moved very slowly by a fine adjustment screw and the instru-

ment is provided with a heavy base for stability. To obtain sharp spectral lines the slit width should

be quite small, about 0.1-0.3 mm.

The amount by which the visible spectrum spreads out into its constituent colors depends on how

rapidly the refractive index of the prism material varies with the wavelength of the radiation, i.e.

dn/dλ. This quantity is called the dispersion and is of prime importance in spectroscopy, since if the

dispersion is small, radiation of slightly differing wavelengths cannot be resolved into separate and

distinct spectral lines.

4 PROCEDURE

PROCEDURE

•First the telescope has to be focused distant objects i.e infinity and this has to be maintained until

the experiment is over, so as not to refocus again. Then, the cross-wires should be focused by mov-

ing the eye-piece of the telescope. Adjust the Collimator such that the image seen in the telescope is

sharp of the slit without the prism.

•Measuring the Angle of Prism A: Place the prism on the Prism Table and lock the prism table in

the position so the incident beam falls on one of the edges of the prism. Now, move the telescope

and locate the images of the slit and note down the angles. The difference between both the angles

is 2A. Hence, half of the difference will give us A.

•Now, choose an angle of incidence other than the previous chosen one and with eye locate approx-

imately the angle at which the spectrum starts to move in the opposite direction as the prism table is

rotated, and lock the prism table. Now, using the telescope, fix the telescope on one of the spectrum

lines, and then use the fine adjustment for the movement of prism table to move the table so that we

get the precise location of the angle where the line starts to move in the opposite direction, and note

the angle for this.

•Without disturbing anything, remove the prism and get the measure of the angle of the direct image

of the slit in the telescope. The difference between these two angles is the Angle of Minimum

Deviation δm for this spectral line λ .Repeat the same for all the spectral lines that are given by the

mercury lamp.

•From above data we can calculate the refractive index n of the prism for various wavelengths. For

the Calibration Curve, plot a graph of δm versus λ. For the

Dispersion Curve, plot a graph of n versus λ.

•We can also calculate the Cauchy’s constants A and B by doing a least squares fit of the data to the

37

Cauchy Formula . We can also calculate the Resolving Power (R) of the prism us-

ing the two yellow lines of the mercury spectrum as . Where and

5 CALCULATIONS

These data are obtained standard values obtained from books and internet.

•R1-one particular line of the spectrum at the position of minimum deviation

•R2-the reflected ray coming from the prism

•R3-the image of the slit without the prism on the prism table

Angle of minimum deviation

Angle of incidence for minimum deviation

Angle of prism A= 2i−Dm

Refractive index

Measurement for RED light

The μ value = 1.48

38

Measurement for YELLOW light

The μ value = 1.49

Measurement of GREEN light

•The behavior of the Dispersion curve can be seen that the fall is not rapid over these range of

wavelengths, hence, it is not a very heavily sloping line which implies that the dispersion of various

spectral line do not vary a lot from each other i.e which is manifested by the closeness of the refrac-

tive index for the range of wavelengths. It can be observed that the curve is roughly parabolic in na-

ture. The dispersion curve is as follows:

39

Now, if μ be the refractive index of the medium, then by Cauchy’s formula,

Now, we take two arbitrary readings, say for RED and YELLOW light. Then, we put the values of

μ and λ and get two simultaneous equation. We solve for a and b. The values are:

a = 1.42 and b= 23190.125

For verification, we substitute this values in the equation again, but using a different λ value, say of

GREEN light. We get the μ for GREEN light to be 1.50 which is same as the experimental value.

6 RESULTS

Thus, the mean refractive index of the material = 1.504

7 PRECAUTIONS

•It must be ensured that the light rays coming out of collimator are parallel.

Hence, the collimator must be focused properly before the experiment.

•The plane on which the prism rests must be horizontal

•The slit must be as thin as possible in order to avoid diffraction