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

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

To find the unknown wavelength, we can use the formula for the position of the bright fringes:

d sin θ = mλ

where d is the distance between the slits, θ is the angle between the line connecting the slit and the bright fringe and the line perpendicular to the screen, m is the order of the bright fringe (starting from m=0 for the central bright fringe), and λ is the wavelength of the light.

For the overlapping fringes, we have:

d sin θ = mλ_1   (for the light of 570 nm wavelength)
d sin θ = mλ_2   (for the unknown wavelength)

For the 11th bright fringe of the unknown wavelength to overlap with the 11th bright fringe of the 570 nm wavelength, we must have:

11λ_1 = 11λ_2
=> λ_2 = (λ_1 / 11) * 11 = 570 / 11 * 11 
=> λ_2 = 456 nm

Therefore, the answer is choice A) 456 nm.

Two Sources of Light Illuminate a Double Slit Simultaneously