Question

Q. 5: A 60°-prism is used as a dispersive element in spectrographs. A the entrance face of the prism should exit as a collim e element in spectrographs. A collimated beam incident on ace of the prism should exit as a collimated beam. Due to refractive index inhomogeneity and surface figure of entrance and exit surfaces, the transmi 1 entrance and exit surfaces, the transmitted wavefront departs from plane. Suggest an interferometric method to test 60'-prism. (b) Length L is measured using the formula L = (m+8) Show that the uncertainty in length measurement is given by where su, s and se are the standard deviations for length, wavelength and fraction measurement sets respectively

Answer 1

Reference Surface Prism being tested Collimated Beam Return Flat Transmission Flat

(b) Let x= f (a, b) @ i dai= f (da; ,doi) The total deviation of a can be worritten as partial derivatione like dx = (2x). da, dx = (x ) do : 3 (du:) nem ) zda:) + (24) Eco:15 Dividing both sides (M-1): Eldx;) ange Ildai + per {adi) NAT 20W - b N-1 This equation could mimic the standard deviation equation. The standand equation can be rewritten as the variance ( e) of a Edx:) 2 (xi-x)" N-1 Zebu:)". 2.624-3). N-1 - Mow, L= (m+€) À en l momento