First slide

Coherent sources and their importance in interference

Question

In a Young’s double slit experiment, two slits are illuminated by a mixture of two wavelengths $12000 \overset{0}{A}$ and $10000 \overset{0}{A}$ . At 6.0 mm from the common central bright fringe on a screen 2 m away from the slits, a bright fringe of one interference pattern coincides with the bright fringe of other. Calculate the distance (in mm) between the slits.

Moderate

A

1
B

2
C

3
D

4

Solution

$L e t s a y t h e d i s \tan c e o f c o m m o n b r i g h t f r i n g e f r o m C B i s x . A l s o, n^{t h} M a x i m a o f λ_{1} c o i n c i d e s w i t h {(n + 1)}^{t h} M a x i m a o f λ_{2} . x = n λ_{1} \frac{D}{d} = (n + 1) λ_{2} \frac{D}{d} \Rightarrow n \times 12000 = (n + 1) \times 10000 \Rightarrow n = 5 N o w, u s e x = n λ \frac{D}{d} \Rightarrow d = \frac{n λ D}{x} = \frac{5 \times 12000 \times 10^{- 10} \times 2}{6 \times 10^{- 3}} = 2 \times 10^{- 3} m = 2 m m$

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