The Spectrometer

The spectrometer is the instrument that turns “violet bends more than red” into numbers: it measures angles to a fraction of a degree and gives refractive indices to four decimal places.

Three parts#

• Collimator: a tube with an achromatic converging lens at one end and an adjustable slit on a sliding inner tube at the other. Set the slit at the lens’s focus and the light leaves as a parallel beam.
• Prism table: a levelled horizontal platform that rotates about a vertical axis, carrying the prism (or grating) and a circular scale in degrees.
• Telescope: an astronomical telescope focused for parallel rays, with cross-wires and a vernier that reads its angle on the circular scale.

First the collimator, telescope and table are levelled. The telescope is focused on a distant object (for parallel rays), and the slit is moved until its image is sharp in the telescope, so the collimator gives parallel light.

Uses#

The angle of a prism

Lit by a sodium lamp, the prism is placed with its refracting edge toward the collimator, so the beam splits and reflects off both faces. The telescope is turned to catch each reflection on its cross-wire. The angle between the two positions is 2A.

The angle of minimum deviation

Find the refracted image of the slit, then nudge the telescope toward the undeviated direction and turn the table to follow it. At one point the image will go no further: that position gives δm. Remove the prism, sight the slit directly, and the difference of the two readings is the angle of minimum deviation.

Refractive index for each wavelength

Using a source with sharp separate lines (a neon tube, say), measure δm for each colour and compute$\ \mu = \sin\tfrac{A + \delta_m}{2}\big/\sin\tfrac A2$. This maps out μ against λ.