Question

Light of wavelength 670 nm passes through two narrow slits 0.65 mm apart. The screen is 2.40 m away. A second source of unknown wavelength produces its second-order fringe 1.21 mm closer to the central maximum than the 670 nm light. What is the wavelength of the unknown light?

Answer 1

wavelength of unknown light is 480.9 nm

Step-by-step explanation:

given data

wavelength = 670 nm

slits distance = 0.65 mm

screen distance = 2.40 m

second-order fringe = 1.21 mm

central maximum = 670 nm

to find out

wavelength of the unknown light

solution

we know here in constructive interference that

path difference = order of fringe × wavelength

d × sinθ = m ×λ ..........1

here d × sinθ is path difference and m is order of fringe and λ is wavelength and we know here angle is small so

sin(θ) = θ

and tan(θ) = x / l

so here

from equation 1

m ×λ = d × x / l

so x 1 = m ×λ1

× l / d ......................1

and x 2 = m ×λ2

× l / d .......................2

so from equation 1 and 2

x 1 - x 2

∆x = m ×λ1

× l / d - m ×λ2

× l / d

now put here all value and find wavelength λ2

λ2 = 650 - (0.66 ×
`10^(-3)`) × (1.23 ×
`10^(-3)`) / (2 × 2.4 )

λ2 = 650 - 169.125

λ2 = 480.875 nm

so wavelength of unknown light is 480.9 nm