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EXPERIMENT – 4

OBJECT: To determine the resolving power of a plane transmission grating.

APPARATUS:  Spectrometer, micrometer slit, sodium vapour lamp, prism, plane

transmission grating, reading lens and reading lens and reading lamp.

FORMULA USED: The resolving power of the grating is given by

Resolving power =W 

d x

λ 

λ ×  

 λ = average value of the wavelength of two lines

dλ = wavelength difference of the two lines

 x = width of the micrometer slit for just resolving the two lines

W = total width of the ruled surface

PROCEDURE: Mount the grating in its holder and fix it on the prism table in such a

way that the rulings are parallel to the slit of the collimator. Set the grating perpendicular

to the incident beam of light. Mount the micrometer slit in front of the collimator by

keeping its edges parallel to the grating, with the help of three screws provided with it.Create a wide opening at the micrometer slit by way of increasing its width. Displace the

telescope to its either side in order to receive the spectrum of the sodium in the first order.

If the two lines are not resolved, then achieve it by reducing the width of the slit of the

collimator. Now, concentrate on the two D lines. Decrease the width of the micrometer

slit. In doing so the two yellow lines will become less distinct and at a particular width of

the micrometer slit the two lines will just merge into a single line. Note the readings of

the micrometer slit under this condition. On further reducing the width of the micrometer

slit a condition will be noticed at which the field of view of the telescope will be

completely dark. Note the reading of the micrometer slit under the condition. The

difference in the two reading of the micrometer slit in the two conditions gives the value

of  x, the optimum width of the grating for just resolving the two D lines. Repeat the

 process several times in order to get a more accurate value of  x. Turn the telescope in

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order to obtain the spectrum in the second order. You will observe that the two lines in

this order are less intense and wider as compared to that of the first order. By following

the above procedure determine the optimum width ' x  of the grating for just resolving the

two lines in the second order. Repeat the process several times in order to get a more

accurate value of ' x  the width of the slit in the second order.

OBSERVATIONS: 

Width of the ruled surface of the grating W  = …cm.

Least count of the micrometer slit = …cm.

Order of

spectrum

N

S.N

Micrometer reading

(cm)

Mean valueWhen thelines are

 just

resolved

( a)

When thefield of view

becomes

dark

( b)

AppropriateValue of

width

 x =  a~ b 

1

1

23

4

5

2

123

4

5

CALCULATION: λ average = 5893 Ǻ, dλ =6 Ǻ (For sodium D lines),  x = …cm.

Resolving power in the first order. =av

  W 

d x

λ 

λ ×  

=5893

6×W 

 x 

= …

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Resolving power in the second order =5893

6×W 

 x 

PROBABLE ERROR: Resolving power P is given by

P =av

  W K 

d x a b

λ 

λ ⋅ =

 

Where K=av

λ  W/dλ is constant, a  and b  are the micrometer slit readings, in the two

conditions. Taking logarithm of both sides of this equation and differentiating it for

maximum probable error we get

dP da db

P a b

+

=

 

 Note that

da =db =dx =least count of the micrometer slit

2...

PdxdP

a b= =

 

RESULT: The resolving power of grating

... for frist order 

=... or second order 

=

 

SOURCES OF ERROR AND PRECAUTIONS:

1.  The mechanical and optical, adjustments of the spectrometer are to be made

carefully.

2.  The micrometer slit should be kept parallel to the spectrometer slit and should be

attached to the collimator.

3.  The condition of just resolution of two lines should be obtained carefully.

4.  Micrometer slit should be moved in one direction.