A light source, which emits two wavelengths and , is used in a Young's double slit experiment. If recorded fringe widths for and are and and the number of fringes for them within a distance on one side of the central maximum are and respectively,

Question

A light source, which emits two wavelengths $λ_{1} = 400 nm$ and $λ_{2} = 600 nm$ , is used in a Young's double slit experiment. If recorded fringe widths for $λ_{1}$ and $λ_{2}$ are $β_{1}$ and $β_{2}$ and the number of fringes for them within a distance $y$ on one side of the central maximum are $m_{1}$ and $m_{2}$ respectively, then [2014]

Smart Achievers · Accepted Answer

(1, 2, 3)

We know that fringe width, $β = \frac{λ D}{d}$

$∵$ $λ_{2} > λ_{1}$

$β_{1}$ $β_{2} > β_{1}$

Number of fringes in a given width, $m \propto \frac{1}{β}$

$∴$ $m_{1} > m_{2}$

$3 \times \frac{λ_{2} D}{d} = \frac{(2 \times 5 - 1) λ_{1} D}{2 d}$

$3 \times 600 = 4.5 \times 400$

Angular separation, $\frac{λ}{d} \propto λ$

So, it is greater for $λ_{2}$

Solution

1 $β_{2} > β_{1}$

2 $m_{1} > m_{2}$

3 From the central maximum, $3^{rd}$ maximum of $λ_{2}$ overlaps with $5^{th}$ minimum of $λ_{1}$

4 The angular separation of fringes for $λ_{1}$ is greater than that for $λ_{2}$

Want Us to Email you About Special Offers & Updates?

Solution

1 β2>β1

2 m1>m2

3 From the central maximum, 3rd maximum of λ2 overlaps with 5th minimum of λ1

4 The angular separation of fringes for λ1 is greater than that for λ2

Ans. (1, 2, 3) We know that fringe width, β=λDd ∵ λ2>λ1 ∴ β2>β1 Number of fringes in a given width, m∝1β ∴ m1>m2 3×λ2Dd=(2×5-1)λ1D2d 3×600=4.5×400 Angular separation, λd∝λ So, it is greater for λ2

Want Us to Email you About Special Offers & Updates?

1 $β_{2} > β_{1}$

2 $m_{1} > m_{2}$

3 From the central maximum, $3^{rd}$ maximum of $λ_{2}$ overlaps with $5^{th}$ minimum of $λ_{1}$

4 The angular separation of fringes for $λ_{1}$ is greater than that for $λ_{2}$