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You perform a double‑slit experiment in order to measure the wavelength of the new laser that you received for your birthday. You set your slit spacing at 1.03 mm and place your screen 8.49 m from the slits. Then, you illuminate the slits with your new toy and find on the screen that the tenth bright fringe is 4.69 cm away from the central bright fringe (counted as the zeroth bright fringe). What is your laser's wavelength expressed in nanometers?

Respuesta :

Manetho

Answer:

[tex]\lambda = 6.25\times10^{-9}[/tex]= 625 nm

Explanation:

We now that for

for maximum intensity(bright fringe) d sinθ=nλ n=0,1,2,....

d= distance between the slits, λ= wavelength of incident ray

for small θ, sinθ≈tanθ= y/D where y is the distance on screen and D is the distance b/w screen and slits.

Given

d=1.19 mm, y=4.97 cm,  and,   n=10,   D=9.47 m

applying formula

λ= (d*y)/(D*n)

putting values we get

[tex]\lambda = \frac{1.19\times10^{-3}\times4.97\times10^{-2}}{9.47\times10}[/tex]

on solving we get

[tex]\lambda = 6.25\times10^{-9}[/tex]= 625 nm

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