SATHEE: Optics 6 Question 38

Optics 6 Question 38

40. White light is used to illuminate the two slits in a Young’s double slit experiment. The separation between the slits is $b$ and the screen is at a distance $d (≫> b)$ from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths are

(1984, 2M)

(a) $λ = b^{2} / d$

(b) $λ = 2 b^{2} / d$

(d) $λ = 2 b^{2} / 3 d$

Show Answer

Solution:

At $P$ (directly infront of $S_{1}) y = b / 2$

$∴$ Path difference,

$Δ X = S_{2} P - S_{1} P = \frac{y \cdot (b)}{d} = \frac{\frac{b}{2} (b)}{d} = \frac{b^{2}}{2 d}$

Those wavelengths will be missing for which

$\begin{aligned} Δ X & = \frac{λ_{1}}{2}, \frac{3 λ_{2}}{2}, \frac{5 λ_{3}}{2} \dots \\ λ_{1} & = 2 Δ x = \frac{b^{2}}{d} \\ λ_{2} & = \frac{2 Δ x}{3} = \frac{b^{2}}{3 d} \\ λ_{3} & = \frac{2 Δ x}{5} = \frac{b^{2}}{5 d} \end{aligned}$

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Optics 6 Question 38

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