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Sagot :
The width and the separation of the two slits are 15μm and 45μm.
What is wavelength?
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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