A screen containing two slits 0.100mm apart is 1.50m from a viewing screen. Light of wavelength 633nm falls on the slits. Approximately how far apart are the bright fringes on the viewing screen?

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A screen containing two slits 0.100mm apart is 1.50m from a viewing screen. Light of wavelength 633nm falls on the slits. Approximately how far apart are the bright fringes on the viewing screen?

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DeniceSandidge DeniceSandidge · Answer 1 · 2025-03-24T10:17:59-04:00

Answer:

distance = 9.495 mm

Step-by-step explanation:

Given data

slits distance = 0.100 mm

viewing screen distance = 1.50 m

wavelength = 633 nm

to find out

how far apart are the bright fringes on the viewing screen

solution

we use here double slit diffraction condition that is

d sin(θ) = m λ .......................1

here m = 0, 1 , 2 , 3 .....

and here for θ small so

sin(θ) = tan(θ) = [tex]\frac{x}{l}[/tex]

so x = l sin (θ)

so from equation 1

x = [tex]\frac{m\lambda l}{d}[/tex]

and

x1 = [tex]\frac{\lambda l}{d}[/tex] ...............2

x2 = [tex]\frac{2\lambda l}{d}[/tex] ..............3

so distance x2 - x1 will be

distance = [tex]\frac{\lambda l}{d}[/tex]

distance = [tex]\frac{633*10^{-9}*1.5}{0.1*10^{-3}}[/tex]

distance = 9.495 mm