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Question
Answer in brief:
In a double-slit arrangement, the slits are separated by a distance equal to 100 times the wavelength of the light passing through the slits.
- What is the angular separation in radians between the central maximum and an adjacent maximum?
- What is the distance between these maxima on a screen 50.0 cm from the slits?
Solution
Data: d = 100λ, D = 50.0 cm
The conditions for maximum in Young's experiment is given by:
d sin (θ) = n λ, n = 0, 1, 2...
the angle between the central maximum and it's adjacent can be determined by setting m equals to 1, so:
d sin (θ) = λ
θ = sin-1 `(λ/"d")`
θ = sin-1 `(λ/(100 λ))`
θ = sin-1 `(1/100)`
θ = 0.01 rad
The distance between the central axis and the first maximum is given by:
D sin θ = D`(lambda/"d")`
= (50.0 cm)`(lambda/(100 lambda))`
= 0.50 cm
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