First slide

Coherent sources and their importance in interference

Question

Two slits separated by a distance of 1 mm are illuminated with red light of wavelength 6.5 $\times$ 10^-7 m. The interference fringes are observed on a screen placed at 1 m from the slits. The distance between the third dark fringe and the fifth bright fringe is equal to

Moderate

A

0.65 mm
B

1.63 mm
C

3.25 mm
D

4.88 mm

Solution

Here, $d = 1 mm = 10^{- 3} m$
$\begin{array}{l} λ = 6 .5 \times 10^{- 7} m \\ D = 1 m \end{array}$
Now, $x_{5} = nλ \frac{D}{d} = 5 \times 6 .5 \times 10^{- 7} \times \frac{1}{10^{- 3}}$
$= 32.5 \times 10^{- 4} m$
and $x_{3} = (2 n - 1) \frac{λ}{2} \frac{D}{d}$
$\begin{array}{l} = \frac{(2 \times 3 - 1) \times 6 .5 \times 10^{- 7}}{2 \times 10^{- 3}} \\ = 16 .25 \times 10^{- 4} m \end{array}$
$\begin{array}{l} ∴ x_{5} - x_{3} = (32 .5 - 16 .25) 10^{- 4} m \\ = 16 .25 \times 10^{- 4} m = 1 .63 mm \end{array}$

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