Question

In Young’s double-slit experiment, 62 fringes are seen in the visible region for sodium light of wavelength 5893 Å. If violet light of wavelength 4359 Å is used in place of sodium light, then what is the number of fringes seen?

Answer 1

From young’s double slit experiment,

λ₁ = 5893 Å ; λ₂ = 4359 Å

${\displaystyle \frac{{\text{n}}_1{\lambda }_1\text{D}}{\text{d}}=\frac{{\text{n}}_2{\lambda }_2\text{D}}{\text{d}}}$

The above condition is total extent of fringes is constant for both wavelengths.

${\displaystyle \frac{62\times 5893\times {10}^{-10}\times \text{D}}{\text{d}}=\frac{{\text{n}}_2\times 4359\times {10}^{-10}\times \text{D}}{\text{d}}}$

${\displaystyle {\text{n}}_2=\frac{62\times 5893}{4359}=\frac{365366}{4359}=83.8}$

${\displaystyle {\text{n}}_2=84}$