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Q.

Young's double slit experiment is conducted with white light $(4000 A^{\circ} - 7000 A^{\circ}) .$ As shown in the diagram, the slit separation $d = (\frac{1}{2}) mm,$ and the screen slit distance, $D = 1$ m. The upper slit is covered with a film of thickness, $t = 1 μm$ having a refractive index, $μ = \frac{3}{2} .$ Find the number of wavelengths which will form a maxima at $y = 3 mm.$

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Detailed Solution

For maxima at P, path difference $= n λ, n =$ integer

$\Rightarrow (s_{2} P - s_{1} P) - (μ - 1) t = n λ \Rightarrow y \frac{d}{D} - (μ - 1) t = n λ$

$\Rightarrow n λ = 10^{- 6} m \Rightarrow n = \frac{10^{- 6}}{λ}$

$n^{max} = \frac{10^{- 6}}{4000 \times 10^{- 10}} = 2.5 & n^{min} = \frac{10^{- 6}}{7000 \times 10^{- 10}} = 1.42$

$∴ n = 2, ∴$ only one wavelength will give maxima at P for $n = 2 .$

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Young's double slit experiment is conducted with white light (4000A∘−7000A∘). As shown in the diagram, the slit separation d=(12)mm, and the screen slit distance, D=1 m. The upper slit is covered with a film of thickness, t=1 μm having a refractive index, μ=32. Find the number of wavelengths which will form a maxima at y=3 mm.