In Young’s double-slit experiment, using sodium light λ = 5898 Ȧ, 85 fringes are seen. If another colour (λ = 5461 Ȧ) is used then find the number of fringes.

Concept:

Young's Double Slit Experiment:

• Monochromatic light (single wavelength) falls on two narrow slits S1 and S2 which are very close together act as two coherent sources, when waves coming from two coherent sources, (S1, S2) superimposes on each other, an interference pattern is obtained on the screen.
• In Young's Double Slit Experiment alternate bright and dark bands obtained on the screen. These bands are called Fringes.
• The separation between any two consecutive bright or dark fringes is called fringe width.
• In Young's Double Slit Experiment all fringes are of equal width.

\(\beta = \frac{{D\lambda }}{d}\)

Where d = Distance between slits

D = Distance between slits and screen

λ =  Wavelength of monochromatic light emitted from the source

Calculation:

Given - Wavelength of sodium light (λ) = 5898 Ȧ, number of fringes (n₁) = 85 and Wavelength of another light (λ) = 5461 Ȧ

In Young's Double Slit Experiment all fringes are of equal width.

\(\beta = \frac{{D\lambda }}{d}\)

If n fringes are formed on the screen, then fringe width will be:

\(n\beta = \frac{{D\lambda }}{d}\)

\( n_1\beta_1 =n_2\beta_2\)

η₁ λ₁ = η₂ λ₂

\( \frac{{{\eta _1}}}{{{\eta _2}}} = \frac{{{\lambda _2}}}{{{\lambda _1}}}\)

\( n_2 = \frac{{5898}}{{5461}}\times 85=91\)