Spectrometer
A spectroscope/spectrometer is an optical instrument which is used for observing pure spectra of sources of light in the laboratory. It is also used for determining of refractive index of a transparent refracting material like glass, water etc.
Three main parts of spectrometer are:
1. Collimator 2. Prism table 3. Telescope.
(a) Collimator provides a parallel beam of light. It consists of two co-axial cylindrical tubes; one can slide inside the other by rack and pinion arrangement R1. The free end of inner tube carries a slit S of adjustable width and free end of outer tube carries an achromatic lens combination L.
The slit is illuminated by the source. When the slit is at the focus of L1, a parallel beam of light is given out.
(b) Prism table is a horizontal metallic circular plate P on which the prism is mounted horizontally on a vertical stand of adjustable height. The free end of the stand lies at the centre of main circular scales S graduated in degrees from 0° to 360°. The two diametrically opposite verniers, V1 and V2 enable us to read accurately the position of the prism.
(c) Telescope is mean t for observing the spectrum. It is usually an astronomical telescope with objective lens L2 and Ramsden eye piece E. it is mounted horizontally on a vertical attached to the main circular scale. The telescope can be roated about the prism table.
A schematic top view of spectroscope is shown in fig. 1
Setting the spectrometer
1. Setting the telescope: turn the telescope towards a distant vertical object. Move the rack and pinion arrangement, R2 of the telescope so that image of the distant object is clearly seen in the telescope. The telescope is thus set for parallel rays. This setting is not to be disturbed throughout the experiment.
2. Setting the collimator: turn the telescope so as to bring it in line with the collimator with the source of the rack and pinion arrangement, R1 of the collimator, till a clear image of the slit is seen. The collimator is thus set to provide a parallel beam of light, which is received by the telescope.
3. Setting the prism: to set the prism in minimum deviation position, place the prism ABC collimator falls on the face BAB at an acute angle. Look for the spectrum through the face AC. Rotate the prism table gradually. The spectral prism table, ∠i changes. Therefore, angle of deviation δ changes. For a particular position of the prism, the spectral lines become stationary. If we rotate the prism table further in the same direction, the spectral lines are seen to turn in the opposite direction. Fix the prism table, where the spectral lines appear stationary. This is the position of minimum deviation.
Turn the telescope to the position T1 so seen is a pure spectrum. The course of rays for a pure spectrum is shown in fig.1
Determination of refractive index µ of material of a prism
The refractive index of the material of a prism is given by
µ = [sin (A + δm)/2]/sinA/2
Where A is the angle of the prism and δm is the angle of minimum deviation.
Hence for the determination of µ of the prism, we must determine δm and A.
(i) Determination of ‘δm’: set the prism in the minimum deviation position as explained above. Turn the telescope so that it’s cross wire coincides with the mean (yellow) color of the spectrum, as in the positionT1. Note this position of telescope to the position T2, so as to focus the image of the slit directly till it coincides with the cross wire of telescope. Read this position of the telescope again. The differences between the two positions of the telescope gives us the angle of minimum deviation, δm.
(ii) Determination of ‘A’: to determine the angle of prism (A), place the prism ABC on the prism table, such that light from the collimator falls symmetrically on the faces AB and AC. Set the telescope in position T1 so that cross wire coincides with the brightest image of the slit from face AB. Turn the telescope to the position T2, so as to coincide the brightest image of the slit from face AC with the vertical cross wire. Let θbe the angle through which telescope is turned.
Then, A = θ/2
Knowing δm and A, refractive index (µ) of the material of the prism can be calculated, using prism formula.
µ of a transparent liquid
The refractive index of a transparent liquid can also be determined using a spectrometer. For this, we take a hollow prism with very thin glass walls. The prism is filled with the liquid whose µ is to be determined. The angle of prism, A and angle of minimum deviation, δm for the liquid prism are measured as explained above for the solid prism.
Hence µ of a transparent liquid can be calculated, using the same prism formula.
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