Wave Optics Part 1

In a Young’s double slit experiment for interference pattern, the position of bright fringe is given by
yn=

nλD

d

Here, D = 1.5 m,
d=0.3×10−3×m
and n = 1
λ=

ynd

D

For first violet, yn=2‌mm=2×10−3m
∴λviolet=2×10−3

d

D

For first red yn=3.5‌mm=3.5×10−3m
λred=3.5×10−3‌

d

D

The difference in wavelengths of red and violet light is
Δλ=λred−λviolet
=3.5×10−3

d

D

−2×10−3‌

d

D

=

d

D

(1.5)×10−3
=

0.3×10−3

1.5

×1.5×10−3
=0.3×10−6
=0.3×10−6×103×10−3
=300×10−9
=300‌nm