Answer:
λ_4 = 450 nm
Explanation:
Given:
- Orange light of wavelength λ_3 = 600 nm
- Light of unknown wavelength = λ_4
- The m = 4 bright fringe of unknown wavelength overlaps m = 3 of orange fringe.
Find:
What is the unknown wavelength?
Solution:
- The condition for bright fringes is given by:
d*sin(Q) = m*λ , m = 0, 1 , 2, 3 , 4 , ...
- For the orange light ( λ = 600 nm ) , we get the m = 3 fringe,
d*sin(Q_3) = 3*(600 nm)
- For the unknown wavelength , we get the m = 4 fringe,
d*sin(Q_4) = 4*(λ_4)
- Since, the position of these fringes are the same:
Q_3 = Q_4
- Hence, 3*(600 nm) = 4*(λ_4)
(λ_4) = 3*600 / 4
λ_4 = 450 nm
