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Question
In a double-slit experiment using the light of wavelength 600 nm, the angular width of the fringe formed on a distant screen is 0.1°. Find the spacing between the two slits.
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Solution 1
The angular width (θ) of the fringe in the double-slit experiment is given by,
`theta=lambda/"d"`
Where
d = Spacing between the slits
Given:
The wavelength of light, λ = 600 nm
The angular width of the fringe,
θ = 0.1° = `pi/1800` = 0.0018 rad
∴ d = `lambda/theta`
d = `(600xx10^(-9))/(18xx10^(-4))`
d = 0.33 × 10−3 m
Solution 2
Wavelength of light used, λ = 6000 nm = 600 × 10−9 m
Angular width of fringe, θ = 0.1° =` 0.1 xx pi/180 = 3.14/1800 "rad"`
The angular width of a fringe is related to slit spacing (d) as:
θ = `lambda/"d"`
`"d"= lambda/θ`
= `(600 xx 10^(-9))/(3.14 /1800)`
= 3.44 × 10−4 m
Therefore, the spacing between the slits is 3.44 × 10−4 m.
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