The width and the separation of the two slits are 15μm and 45μm.
<h3>What is wavelength?</h3>
The wavelength is the distance between the adjacent crest or trough of the sinusoidal wave.
Given is the laser light of wavelength λ= 500.0 nm = 500x 10⁻⁹ m illuminates two identical slits, producing an interference pattern on a screen D =90.0 cm from the slits. the bright bands distance Δy = 1.00 cm apart, and the third bright bands on either side of the central maximum are missing in the pattern.
If d = separation between the two slits and a is the width of the slit
dsinθ/asinθ =m(max) λ/ m(min)λ
d/a = m(max) / m(min)..................(1)
where m(max)= ±3.0 and m(min)=1.0
So, d.a = 3
The distance from the central maxima to the third minimum fringe
y₃ = 3Δy
and the angle formed is
tan θ₃ = y₃/D or 3Δy/D
Put the values, we get
θ₃ =1.91°
From the equation, a sinθ = m(min)λ
a = 1 x 500 x 10⁻⁹/sin 1.91
a = 15 x 10⁻⁶ m or 15μm
From the equation, dsinθ= m(max) λ
d = 3 x 500 x 10⁻⁹/sin 1.91
d = 45 x 10⁻⁶ m or 45μm
Thus, the separation and the width are 45μm and 15μm
Learn more about wavelength.
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