First slide

Young's double slit Experiment

Question

In Young's double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths $λ_{1} = 12000 \overset{0}{A}$ and $λ_{2} = 10000 \overset{0}{A}$ . At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

Moderate

A

4 mm
B

3 mm
C

8 mm
D

6 mm

Solution

$L e t n_{1} b r i g h t f r i n g e o f λ_{1} c o i n c i d e s w i t h n_{2} b r i g h t f r i n g e o f λ_{2} T h e n \frac{n_{1} λ_{1} D}{d} = \frac{n_{2} λ_{2} D}{d} o r n_{1} λ_{1} = n_{2} λ \frac{n_{1}}{n_{2}} = \frac{λ_{2}}{λ_{1}} = \frac{10000}{12000} = \frac{5}{6}$
Let x be given distance. $∴ x = \frac{n_{1} λ_{1} D}{d}$
Here, $n_{1} = 5, D = 2 m, d = 2 m m = 2 \times 10^{- 3} m$
$λ_{1} = 12000 A^{0} = 12000 \times 10^{- 10} m = 12 \times 10^{- 7} m x = \frac{5 \times 12 \times 10^{- 7} m \times 2 m}{2 \times 10^{- 3} m} = 6 \times 10^{- 3} m = 6 m m$

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