A pair of narrow slits separated by a distance is illuminated by light of wavelength

PHYSICS · Subjective · A Level · Physics · Waves · Waves

Problem

A pair of narrow slits separated by a distance

d

is illuminated by light of wavelength

\lambda

. The interference pattern is viewed on a screen at a distance

D

from the slits (

D \gg d

). (a) Derive an expression for the maximum possible number

N_b

of complete bright fringes whose centres lie between the points

y=-L

and

y=+L

on the screen, where

L

is any positive distance measured from the central bright fringe. (b) In an experiment

d=0.30\,\text{mm}

and

D=1.8\,\text{m}

. For light of wavelength

540\,\text{nm}

the segment

(-L, +L)

contains 25 complete bright fringes. Find the value of

L

. (c) The slit separation is now kept unchanged, but the source is replaced by another of wavelength

450\,\text{nm}

. Keeping the same value of

L

, calculate the new number of complete bright fringes that will now lie within the segment.