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2 years ago

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Monochromatic light is incident on two slits separated by 0,2 mm. An interference pattern is observed on a screen 3,7 m away. Th

e distance between the 3rd dark fringe and the central antinode is 0,048 What is the wavelength of the light? Write your answer in sicentific notation or in decimal form

1 answer:

zalisa [80]2 years ago

5 0

Answer:

λ = 864 nm

Explanation:

To find the wavelength of the light you use the following formula, which determines the position of the m-th fringe in an interference pattern:

$y_m=\frac{m\lambda D}{d}$ (1)

ym: position of a bright fringe

D: distance from the slits to the screen = 3,7 m

d: distance between slits = 0,2mm = 0,2 *10^-3 m

m: order of the fringe

λ: wavelength of the light

You have the distance from the central peak to the third fringe (0,048m). Then, you can use the equation (1) with m=3 and solve for the wavelength:

$y_3=\frac{3\lambda D}{d}\\\\\lambda=\frac{dy_3}{3D}=\frac{(0,2*10^{-3}m)(0,048m)}{3(3,7m)}=8,64*10^{-7}m\\\\\lambda=864*10^{-9}m=864nm$

henc, the wavelength of the light is 864nm

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