Q.Explain the experimental determination of the refractive index of the material of a prism using a spectrometer.

A spectrometer is a precision instrument used to study the spectra emitted by different light sources and to measure the refractive indices of transparent materials, built from three main parts: the collimator, a rigid tube with a convex lens at its inner end and an adjustable-width vertical slit (kept at the lens's focal point) at the outer end, producing a truly parallel beam of light; the prism table, a levelled, rotatable platform (with three levelling screws) on which the prism or grating under study is mounted, rotatable about a vertical axis and readable via two verniers; and the telescope, an astronomical-type instrument with cross-wires and an adjustable eyepiece, mounted on a rotating, graduated circular scale, used to view and precisely locate refracted or diffracted images. Before any measurement, four preliminary adjustments are made in sequence: focusing the eyepiece on its own cross-wires; adjusting the telescope to receive and focus parallel rays (by sighting a distant object); adjusting the collimator so its slit sits exactly at the lens's focus (producing a sharp image through the parallel-focused telescope); and levelling the prism table with a spirit level and its levelling screws. To measure the prism angle $A$: with the prism's refracting edge facing the collimator, the telescope is turned in turn to catch the slit's image reflected off each of the two refracting faces; the angle the telescope turns through between these two readings is $2A$, so $A$ is half that turned angle. To measure the an …