Question

Consider a pair of slits separated by 1.001.00 micrometers. What is the angle θredθredtheta_red to the interference maximum with m=1m=1 for red light with a wavelength of 700700 nanometers? Express your answer in degrees to three significant figures.

Answer 1

Right formatted question:

Consider a pair of slits separated by 1.00 micrometers. What is the angle $\theta_{red}$ to the interference maximum with m=1 for red light with a wavelength of 700 nanometers? Express your answer in degrees to three significant figures.

Answer:

The angle is 44.43 degrees

Explanation:

This is Young's double slit experiment where a monochromatic light is passed through two small slit with a small distance between them, and the projection obtained on a screen placed at a distance D from the slits is an interference pattern with maximus and minimums distributed on the screen. The equation that describes this phenomenon is:

$d\sin \theta = m\lambda$ (1)

with λ the wavelength, θ the angular position of the m interference maximum, d the distance between the slits and m the number of the interference maximum. Solving (1) for θ for red light:

$\theta_{red} =\arcsin (\frac{m\lambda}{d})=\arcsin (\frac{1*700\times10^{-9}}{1.00\times10^{-6}})$

$\theta_{red}=44.43 degrees$