Question

A light source emits visible light of two wavelengths  λ₁  = 420 nm and  λ₂ = 520 nm . The source is used in a double-slit interference experiment in which D =100 cm and d = 0.025 mm which of the following statement are correct for the interference fringes?

(a)  Central bright fringes due to λ₁ and λ₂ overlap

(b)  First interference maximas of λ₁ and λ₂ are separated by 0.4 cm 

(c)  42^nd bright fringe of λ₂ overlap with 52^nd bright fringe of λ₂ 

(d)  on the screen, the bright fringes from λ₁ and λ₂ overlap exactly at 87.4 cm

Answer 1

Correct option  (a), (b), (c) and (d) 

Explanation:

(a) At position O the path difference is always zero, irrespective of wavelength as path difference = d sinθ

for central maxima, θ = 0 , thus central bright fringes due to λ₁ and λ₂ overlap

Thus 52^nd bright fringe of the 420 nm light overlap with 42nd bright fringe of the 520 nm light 

(d)  To find the value of y for these fringes