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.

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

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