AIM:- To determine wavelength of spectral lines using plane-transmission grating.

APPARATUS :- Plane transmission grating with its holder, spectrometer, sodium vapour lamp, prism.

FORMULA :-

Lamda = (a+b) sin (theta)_n / n

where lamda is wavelength of sodium light,
(a+b) is grating element and (a+b) = 2.54/no. of lines per inch,
(theta)_n = angle of diffraction of n th order,
and n is order of spectrum.

FIGURE :-

PROCEDURE:-

The spectrometer is set with its collimator towards the source of light. The telescope is brought in line with the collimator. The width of the slit is made sufficiently narrow. The spectrometer is levelled with with the help of spirit level such that the image of slit is at the centre of the field of view. The eyepiece of the telescope is adjusted so that cross wires are distinctly visible. The crosswire tube is rotated such that the vertical crosswire coincides with the image of the slit is obtained. Using a glass prism, the optical levelling of the prism table is done. Following Schuster’s method, the collimator and telescope are adjusted for parallel rays. The least count of the instrument is determined . It is taken care that adjustments of the spectrometer are not disturbed subsequently during the experiment.

As the formula is derived for the case where light is incident perpendicular to the face of the grating, it is essential that the grating is to be set on the prism table with its plane normal to the axis of the collimator. The setting is achieved through the following steps. The telescope is brought in line with the collimator to have image of the slit on the vertical cross wire. It is locked in that position. The lower screw of the spectrometer is unlocked and tha table is rorated till the reading on one vernier is exactly 360 degrees. The reading on the second vernier is therefore 180 degrees. The screw is locked. Now the telescope arm is unlocked and ratated through 90 degrees in clockwise or anticlockwise direction. It is locked in that position. The grating stand is mounted on the prism table and the grating is placed in it with its ruled surface towards the telescope. Care is taken that the grating stands at the centre of the prism table. Then the prism table is rotated slowly so that a reflected image is seen in the field of view of the telescope. Rotating the prism table very slowly the reflected image to coincide exactly with the vertical crosswire. In this position, the angle of incidence of light on the grating surface is 45 degrees. The reading of the position of the prism table is noted down. The prism table is rotated from the above position through 45 degrees more so that the grating plane becomes normal to the direction of light. The prism table is locked in this position. This is the normal incidence position.

The telescope is then unlocked and rotated to bring it in line with the collimator to receive the white image of the slit on the crosswires. The reading of the position of the telescope is noted. The telescope is slowly rotated to right till the violet image of the slit corresponding to the first order is coincided with the crosswire. In this position, the reading of the scale is noted. The difference between the two positions gives the angle of deviation of violet colour belonging to the first order (m = 1). The telescope is moved slowly and the vertical crosswire is coincided successively with other colours belonging to the first order and the respective positions are noted down. The telescope is rotated further right to get the images belonging to the second order. The above procedure is repeated and the positions of the various spectral lines are noted down in table. Now the telescope is brought to the left side of the centrel white line. It is moved slowly to the left to get the images belonging to the first order and then second order. The observations are recorded in table. Using the formula, the wavelengths of variuos spectral lines are calculated.

OBSERVATIONS:-

CALCULATIONS:-

Lamda = (a+b) sin (theta)_n / n

For the first order spectrum, n = 1
So lamda = (a+b) sin (theta)
So lamda =       A⁰.

For the second order spectrum, n = 2
So Lamda = (a+b) sin (theta) / 2
So lamda =       A⁰.

RESULT:-

The wavelength of yellow line of sodium light is       A⁰.

PRECAUTIONS:-

1. The prism table should be properly levelled.
2. Grating surface is never touched while handling it.
3. Grating should be mounted with its lines parallel to the slit or vertical wire of the cross wires.
4. Prism table should not be disturbed while rotating the telescope to receive images of different orders.
5. Telescope should be rotated slowly, otherwise there is a possibility of missing an order.