Find the value of lambda_2.

jlo2ni5x 2022-07-18 Answered
In a single slit diffraction, first minimum for green light of wavelength 5240   A ˙ coincides with first maximum of some other wavelength λ 1 '. Find the value of λ 1 .
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Answers (1)

Kaiden Weeks
Answered 2022-07-19 Author has 14 answers
Since, Between the first and second minima, there is a maxima of undetermined wavelength.
And,
Position of minima in diffraction Pattern is
n λ = d sin θ
Thus, For first minima of Green Light of wavelength λ g will be,
n λ g = d sin θ 1
To Calculate
The first maxima of some other wavelength λ 1 will be at position,
3 2 λ 1 = d sin θ 2
For the first minimum of diffraction Pattern of Green light
n λ g = d sin θ 1
For the first maxima of some other light of wavelength λ 1
3 2 λ 1 = d sin θ 2
Since, first minimum of green light coincide with the first maximum of the other light therefore,
θ 1 = θ 2 thus sin θ 1 = sin θ 2
Therefore we can write it as,
3 2 λ 1 = n λ g
Given:
n=1 (for first minima)
λ g = 5240   A ˙ 3 2 λ 1 = 1 ( 5240 A ˙ ) λ 1 = 2 × 5240 A ˙ 3 λ 1 = 3493 A ˙
The Wavelength of the first maxima of some other light is λ 1 = 3493 A ˙
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