Find the refractive index of the material of a prism using spectrometer

Apparatus:
Spectrometer, glass prism and sodium lamp

Theory:
Spectrometer is an optical instrument used in laboratory to measure wave length of spectral lines, refractive index of solids etc. It has three essential parts.

Collimator:
It consists of a tube of variable length with an adjustable slit S at one end and a convex lens L at the other end. It is fixed to the base of the instrument. When slit is illuminated by light and adjusted at the focal plane of the lens, the collimator produces parallel rays.

Prism Table:
It is a metallic surface with leveling screws on which a prism or a grating may be mounted. It can be fixed to a rotatable central axis at any desired height. The axis carries with it two fixed vernier scales V₁ and V₂ diametrically opposite to each other. When the prism table is rotated, the verniers change their position on a scale marked in degree or half a degree.

Telescope:
It is an astronomical telescope with a pair of cross wires for examining the spectrum. It is capable of rotation about the central axis of the prism table and carries a graduated circular platform marked in degrees or half degrees. It can be locked in any position and with a screw we may give a slight angular movement to it. The position of the telescope may be read by means of the two vernier scales V₁ and V₂.

Alignment and adjustment of the Spectrometer:
Before using this instrument the following steps must be taken to align the spectrometer.

1. The eye piece is focused on the cross wires, so that they are clearly and sharply visible.

2. The telescope is adjusted for parallel rays, so that parallel beam falling on the objective of the telescope produces an image at the cross wires. To achieve this parallax is removed between the image of a far off object and the cross wires.

3. The collimator is adjusted to give parallel beam of light this is done by viewing the image of the slit, illuminated with a monochromatic source of light, in the telescope and removing the parallax between the image of the slit and the cross wires.

Procedure:
1. Make all the required adjustment with the spectrometer and turn on the sodium light or laser light.
2. Find the vernier constant of the spectrometer.
3. Place the prism on the table of the spectrometer so that its refracting edge is vertical and parallel to the slit of the collimator and adjust the collimator to illuminate both the faces of the prism.
4. Keeping the prism table fixed, rotate the telescope to receive the rays AT₁ reflecting from the face AB. Set the cross wire on the middle of the slit image and note the reading indicated by both the vernier scales V₁ and V₂.Let it be T₁.
5. Now rotate the telescope to receive the light rays AT₂ after reflecting from the face AC and set the cross wire on the middle of the slit image and note the readings of the both verniers again. Let it be T₂.
6. Repeat the step 4 and step 5 and take three observations.
7. Angle of the prism is equal to half of the angle between rays AT₁ and AT₂.
8. Now place the prism on the prism table so that its center coincides with the center of the table. Rotate the table so that the light from collimator fells on the face AB and after refraction through the prism emerge from the face AC. View the image through the prism and rotate the table in suitable direction following the image till it becomes stationary. This will happen when the position of minimum deviation is reached. Note the readings of the both verniers. Let it be T₁.
9. Remove the prism and observe the direct image with telescope. Note the readings of the both verniers. Let it be T_4.The difference between two positions of the telescope is the angle of minimum deviation D_m.
10. Take two more readings as explained in step 8 and step 9.
11. Find the refracting index of the prism by formula

Observations & Calculations:
Vernier constant of the spectrometer =………….

No. of obs.	Vernier V1			Vernier V2
	Position of the telescope		Difference	Position of the telescope		Difference
	T3	T4	= T3 –T4	T1	T2	= T3 –T4
1. 2. 3.

Angle of the prism = A =
Mean value of  = ………

No. of obs.	Vernier V1			Vernier V2
	Position of the telescope		Difference	Position of the telescope		Difference
	T3	T4	Dm = T3- T4	T1	T2	Dm = T3- T4
1. 2. 3.

Refractive index of the prism:                                         Mean value of D_m = ……….

Precautions:
1. The width of the slit should be very narrow.
2. Axis of the telescope should be perpendicular to the vertical axis of the spectrometer.
3. The prism table has to be kept firmly fixed while finding the angle of the prism.

4.If verniers pass the zero of the scale as telescope is rotated, this fact should be accounted for in determining the angle turned.