Answer:
a) λ = 666.7 nm, b) infinity, c) d = 2,857 10⁻⁴ m = 0.2857 mm
Explanation:
The interference phenomenon is described by Young's equation
d sin θ = m λ
Where d is the gap separation, λ the wavelength and m the order of interference
Let's use trigonometry for the angle
tan θ = y / L
As in this we express the angles are very small
tan θ = sin θ / cos θ = sin θ
We replace
d y / L = m λ
a) let's look for the wavelength
λ = d y / L m
The first bright strip occurs for m = 1
Let's calculate
λ = 0.1 10⁻³ 2 10⁻² / 3
λ = 6.667 10⁻⁷ m
Let's take nm
λ = 666.7 nm
this is orange to red
.b) In theory the number of strips is infinite, but in the one made it is determined by the convolution with the diffraction pattern of each slit, which depends on the width of each one.
c) If the new distance y = 7 mm
Which of the separation of the slits
d = m λ L / y
d = 1 666.7 10⁻⁹ 3 / 0.007
d = 2,857 10⁻⁴ m = 0.2857 mm
