Question

Monochromatic light is incident on two slits separated by 0,2 mm. An interference pattern is observed on a screen 3,7 m away. The distance between the 3rd dark fringe and the central antinode is 0,048 What is the wavelength of the light? Write your answer in sicentific notation or in decimal form

Answer 1

λ = 864 nm

Step-by-step explanation:

To find the wavelength of the light you use the following formula, which determines the position of the m-th fringe in an interference pattern:

`y_m=(m\lambda D)/(d)` (1)

ym: position of a bright fringe

D: distance from the slits to the screen = 3,7 m

d: distance between slits = 0,2mm = 0,2 *10^-3 m

m: order of the fringe

λ: wavelength of the light

You have the distance from the central peak to the third fringe (0,048m). Then, you can use the equation (1) with m=3 and solve for the wavelength:

`y_3=(3\lambda D)/(d)\\\\\lambda=(dy_3)/(3D)=((0,2*10^(-3)m)(0,048m))/(3(3,7m))=8,64*10^(-7)m\\\\\lambda=864*10^(-9)m=864nm`

henc, the wavelength of the light is 864nm