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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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