1. Young’s double-slit interference experiment
Interference conditions:
- same frequency
- The vibration direction is the same
- Phase difference/optical path difference are the same
Parameter Description:
- The distance between two seams:
d
d
d
- Screen and seam spacing:
D
D
D
- Wavelength:
λ
\lambda
λ
- The distance from the point on the screen to the center point is
x
x
x
I
=
I
1
+
I
2
+
2
I
1
I
2
cos
?
δ
I = I_1 + I_2 + 2I_1 I_2 \cos \delta
I=I1? + I2? + 2I1?I2?cosδ
I
1
=
I
2
=
I
0
I_1 = I_2 = I_0
I1?=I2?=I0?
I
=
4
I
0
cos
?
2
δ
I = 4I_0\cos ^2 \delta
I=4I0?cos2δ
δ
=
2
π
λ
Δ
=
k
Δ
=
k
(
r
2
?
r
1
)
\delta = \frac{2\pi}{\lambda} \Delta = k \Delta = k (r_2 – r_1)
δ=λ2π?Δ=kΔ=k(r2r1?)
Optical path difference:
Δ
=
d
D
x
\Delta = \frac{d}{D}x
Δ=Dd?x
Light intensity changes:
I
=
4
I
0
cos
?
2
(
k
d
2
D
x
)
=
4
I
0
cos
?
2
(
π
d
λ
D
x
)
I = 4 I_0 \cos ^2 (\frac{kd}{2D}x) = 4 I_0 \cos ^2 (\frac{\pi d}{\lambda D}x)
I=4I0?cos2(2Dkd?x)=4I0?cos2(λDπd?x)
2. Matlab implements Young’s double-slit interference experiment
Basic parameter settings:
d = 2e-4; D = 1; lambda = 500e-9; I0 = 1;
According to theoretical calculation, the stripe spacing:
Δ
x
=
D
d
λ
=
2.5
m
m
\Delta x = \frac{D}{d} \lambda = 2.5mm
Δx=dD?λ=2.5mm
Intensity changes of interference fringes:
%% interference intensity change
x = -10:0.01:10;
Intensity1 = 4*I0*cos(pi*d*x*1e-3/(lambda*D)).*cos(pi*d*x*1e-3/(lambda*D));
figure;
plot(x, Intensity1);
xlabel('x/mm');
ylabel('Intensity');
title('Interference fringe intensity change');
Interference fringe drawing:
%% Interference fringe 2D
x = -10:0.01:10;
y = -10:0.01:10;
[X,~] = meshgrid(x,y);
Intensity3 = 4*I0*cos(pi*d*X*1e-3/(lambda*D)).*cos(pi*d*X*1e-3/(lambda*D));
figure;
imagesc(x,y,Intensity3);
colormap('gray');
xlabel('x/mm');
ylabel('y');
title('Interference fringes');
colorbar;
ylabel(colorbar,'light intensity');
