Question

A double slit separation is 3 mm and is illuminated by a white light. A screen is placed 3.0 m away to observe the interference pattern. a) What is the angular separation of the 2nd order red (λ=700 nm) and 3rd order violet (λ=400 nm) bright fringe? b) How high is the 4th order fringe for the yellow color (λ=589 nm) on the screen? c) Is it possible to adjust the slit separation so that for the 1st order red coincides with 2nd order violet bright fringe?

Answer 1

here,

in double slit exp we have :
y = (m * lamda* D) /d --------------(1)

Where,
y = displacement from the centerline for maximum intensity
d is slit seperation = 3mm = 0.003 m
D = distance from slits = 3.0 m
Lamda = wavelength
m = order

SinA = m*lamda/d -----------(2)

A = angular seperation

Case A :

For red :
Lamda= 700 nm = 7 * 10-^7 m
m = 2

From eqn 2 we get :
SinA = (2*7 * 10^-7) / 0.003
A = 0.00047 degrees

For Voilet :
lamda = 400 nm = 4*10^-7m
m = 3

From eqn 2 we get :
SinA = (3*4*10^-7) / 0.003
A = 0.00040 degrees

CASE B:

m = 4
lamda = 589 nm = 5.89 * 10^-7 m

From Eqn 1 :

y = (m * lamda* D) /d
y = (4 * 5.89 * 10^-7 * 3) / 0.003
y = 0.00235 m

CASE C:
m = 1

For red :
Lamda= 700 nm = 7 * 10-^7 m

Calculating y for Red:
From Eqn 1 :
y = (m * lamda* D) /d
y = (1 * 7* 10^-7 * 3) / 0.003
y = 0.0007 m

For Voilet :
lamda = 400 nm = 4*10^-7m

Calculating y for Voilet:
From Eqn 1 :
y = (m * lamda* D) /d
y = (1 * 4* 10^-7 * 3) / 0.003
y = 0.0004 m

not possible as Yred > Yvoilet