Physics 101: Single/Double Slits questions?

Question

1. Find the separation between 2 slits for which 650 nm orange light has its first maximum at 3°.

2. A beam with a wavelength of 450 nm hits one slit producing a central maximum 5 cm wide on a screen 2 m away. Calculate the slit width.

Answer 1

1. λ=650 nm, θ=3°, d=the separation between 2 slits

first maximum: d*sinθ=λ ==>

d=λ/sinθ=650e-09/sin3°=12.42 µm

2. λ=450 nm, z=5/2 cm=0.025 m, L=2m, w=slit width

first minimum: w*sinθ=λ, and sinθ=z/L ==>

w*z/L=λ ==> w=λL/z=450e-09*2/0.025=36 µm