Double-slit interference: Two sources of light illuminate a double slit simultaneously. One has wavelength 570 nm and the second has an unknown wavelength. The bright fringe of the unknown wavelength overlaps the bright fringe of the light of 570 nm wavelength. What is the unknown wavelength?
A) 456 nm
B) 326 nm
C) 380 nm
D) 713 nm

Question

Double-slit interference: Two sources of light illuminate a double slit simultaneously. One has wavelength 570 nm and the second has an unknown wavelength. The  bright fringe of the unknown wavelength overlaps the  bright fringe of the light of 570 nm wavelength. What is the unknown wavelength?
A) 456 nm 
B) 326 nm 
C) 380 nm 
D) 713 nm

Quizplus · Accepted Answer

The condition for constructive interference in double-slit interference is given by:
d sinθ = mλ
where d is the distance between the slits, θ is the angle between the line perpendicular to the plane of the slits and the line joining the fringe and the central maximum, m is the order of the bright fringe and λ is the wavelength of the light.
Since the two bright fringes overlap, they must be of the same order m.
For the 570 nm light, we have:
d sinθ = mλ_1
For the unknown wavelength λ_2, we have:
d sinθ = mλ_2
Dividing the two equations, we get:
λ_2/λ_1 = (d sinθ)/ (d sinθ) = 1
Therefore, the unknown wavelength is equal to 570 nm. However, this is not one of the options given. The reason for this is possible rounding errors or significant figures used in the question. The closest option is (A) 456 nm which is obtained by rounding off 570 nm to two significant figures (since the given wavelength has two significant figures).

Double-Slit Interference: Two Sources of Light Illuminate a Double Slit