Answer to Question #93249 in Optics for Joy

Question

A slit of width a is illuminated by white light
1. For what value of a will the first minimum for red light of wavelength 650nm appear at an angle 15°
2. What is the wavelength of the light whose first side diffraction maximum is at 15°, thus coinciding with the first minimum for the red light.

Answer 1

1. We can write for diffraction minimum

$a \sin θ = mλ (1)$

where a is the slit of width

Using (1) we got

$a=\frac{ mλ }{\sin θ } (2)$

In our case, θ=15°, m=1, λ=650×10^-9 m

Using (2) we got

a=2.5×10^-6 m

Answer

2.5×10^-6 m

2. The first side diffraction maximum can be located by setting m=1.5.

In this case, we can rewrite (1) as

$a \sin θ = 1.5λ (2)$

In our case, a=2.5×10^-6 m, θ=15°

Using (2) we got

λ=430×10^-9 m

Answer

430×10^-9 m