Question

Light of wavelength 600 nm that falls on a pair of slits producing interference pattern on a screen in which the bright fringes are separated by 7.2 mm. What must be the wavelength of another light which produces bright fringes separated by 8.1 mm with the same apparatus?

Answer 1

${\displaystyle \beta =\frac{\lambda \text{D}}{\text{d}}}$

β ∝ λ

${\displaystyle \frac{{\beta }_1}{{\beta }_2}=\frac{{\lambda }_1}{{\lambda }_2}}$

Given: β₁ = 7.2 mm, β₂ = 8.1 mm, λ₁ = 600 nm, λ₂ = ?

${\displaystyle {\lambda }_2=\frac{{\lambda }_1{\beta }_2}{{\beta }_1}}$

${\displaystyle {\lambda }_2=\frac{600\times 8.1}{7.2}}$

λ₂ = 675 nm