First slide

Diffraction

Question

A person sets up Young's experiment using a sodium Iamp and placing two slits 1 metre from a screen' The person is not sure of slit separation and he varies the separation and finds that the interference fringes disappear if the slits are too far apart. The angular resolution of his eye is (1/60). How far apart are the slits when he just cannot see the interference pattern ? $[λ = 5890 Å]$

Difficult

A

2.025 mm
B

1.025 mm
C

4.01 mm
D

5mm

Solution

$θ = \frac{β}{D} = \frac{λ D}{(2 d) D} = \frac{λ}{(2 d)} But θ = \frac{1^{\circ}}{60} = \frac{1}{60} \times \frac{1}{180} \times π radian \frac{1}{60} \times \frac{1}{180} \times π = \frac{λ}{2 d} = \frac{5890 \times 10^{- 8}}{(2 d)} o r 2 d = \frac{(5890 \times 10^{- 8}) \times 60 \times 180}{π} c m \Rightarrow d = 0 \cdot 2025 c m = 2 \cdot 025 m m$

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