A monochromatic light of wavelength falls on two very narrow slits separated by and a…

PHYSICS · Multi-part · A Level · Physics · Waves · Waves

Problem

A monochromatic light of wavelength

550\,\text{nm}

falls on two very narrow slits separated by

d

and a flat screen is kept at a distance

D

from the plane of the slits. Answer the following for this arrangement. (i) Using geometrical considerations, establish the relation between the path difference

\Delta x

of the two interfering waves and the linear distance

y

of a point on the screen from the central maximum under the small–angle approximation. (ii) Hence obtain an expression for the linear position

y_n

of the

n

th bright fringe from the central maximum. (iii) Derive a general expression for the linear distance between the

m

th bright fringe and the

p

th dark fringe on the same side of the central maximum. (iv) Using your result in part (iii), calculate the distance between the

4

th bright fringe and the

6

th dark fringe when

d=0.30\,\text{mm}

and

D=1.80\,\text{m}

. Express your answer correct to two significant figures.

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