Question

Light is incident on a double-slit. the fourth bright band has an angular distance of 7.0° from the central maximum. what is the distance between the slits (in mm)? (assume the frequency of the light is 5.4 ´ 1014 hz.)

Answer 1

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:

$\boxed {d \sin \theta = n \lambda }$

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:

$d \sin \theta = n \lambda$

$d \sin \theta = n \frac{v}{f}$

$d = \frac{ nv } {f \sin \theta}$

$d = \frac { 4 \times 3 \times 10^8 } { 5.4 \times 10^{14} \times \sin 7.0^o }$

$d \approx 1.8 \times 10^{-5} \texttt{ m}$

$d \approx 1.8 \times 10^{-2} \texttt{ mm}$

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Conclusion:

The distance between the slits is about 1.8 × 10⁻² mm

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Answer details

Grade: High School

Subject: Physics

Chapter: Light

Answer 2

Hope this helps just use the 2 equations just follow it through . The number does seem quite big maybe check the values given