The distance between the slits is about 1.8 × 10⁻² mm
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Further explanation
Let's recall the Young's double-slit formula as follows:
[tex]\boxed {d \sin \theta = n \lambda }[/tex]
where:
d = distance between the slits ( m )
θ = angular distance
n = order number
λ = wavelength ( m )
Let us now tackle the problem!
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Given:
angular distance = θ = 7.0°
frequency of the light = f = 5.4 × 10¹⁴ Hz
order number = n = 4
speed of light = v = 3 × 10⁸ m/s
Asked:
distance between the slits = d = ?
Solution:
[tex]d \sin \theta = n \lambda[/tex]
[tex]d \sin \theta = n \frac{v}{f}[/tex]
[tex]d = \frac{ nv } {f \sin \theta}[/tex]
[tex]d = \frac { 4 \times 3 \times 10^8 } { 5.4 \times 10^{14} \times \sin 7.0^o }[/tex]
[tex]d \approx 1.8 \times 10^{-5} \texttt{ m}[/tex]
[tex]d \approx 1.8 \times 10^{-2} \texttt{ mm}[/tex]
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Conclusion:
The distance between the slits is about 1.8 × 10⁻² mm
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Learn more
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Answer details
Grade: High School
Subject: Physics
Chapter: Light
