Question

In a Young's double-slit experiment the separation distance y between the second-order bright fringe and the central bright fringe on a flat screen is 0.0199 m, when the light has a wavelength of 425 nm. Assume that the angles are small enough so that sin is approximately equal to tan . Find the separation y when the light has a wavelength of 583 nm.

Answer 1

separation y when the light has a wavelength of 583 nm is 0.027298 m

Step-by-step explanation:

Given data

central bright fringe L = 0.0199 m

m = 2

wavelength = 425 nm

to find out

separation y when the light has a wavelength of 583 nm

solution

we have given

sin(θ) ≅ cos(θ)

so sin(θ) = mλ /d

and we say tan(θ) = y/L

so in small angle we say

0.0199 /L = 2 ( 425 ) / d

so d/L = 2(425) / 0.0199 .........................a

and

now with wavelength 583 nm

y/L = 2(583) /d

d/L = 2(583) / y ...........................................b

so from a and b

2(583) / y = 2(425) / 0.0199

y = 583 (0.0199) / 425

y = 0.027298 m

separation y when the light has a wavelength of 583 nm is 0.027298 m