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3 years ago

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At sunset, red light travels horizontally through the doorway in the western wall of your beach cabin, and you observe the light

on the eastern wall. Assume that the light has a wavelength of 700 nm, that the door is 1.0 m wide, and that the distance from the door to the far wall of your cabin in 14 m .Part ADetermine the distance between the central bright fringe and a first-order dark fringe of the interference pattern created by the doorway "slit".

1 answer:

Nady [450]3 years ago

6 0

Answer:

$9.8\cdot 10^{-6}m$

Explanation:

For light passing through a single slit, the position of the nth-minimum from the central bright fringe in the diffraction pattern is given by

$y=\frac{n \lambda D}{d}$

where

$\lambda$ is the wavelength

D is the distance of the screen from the slit

d is the width of the slit

In this problem, we have

$\lambda=700 nm = 7.00\cdot 10^{-7}m$ is the wavelength of the red light

D = 14 m is the distance of the screen from the doorway

d = 1.0 m is the width of the doorway

Substituting n=1 into the equation, we find the distance between the central bright fringe and the first-order dark fringe (the first minimum):

$y=\frac{(1)(7.00\cdot 10^{-7} m)(14 m)}{1.0 m}=9.8\cdot 10^{-6}m$

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