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Question
Find the angular separation between the consecutive bright fringes in a Young's double slit experiment with blue-green light of wavelength 500 nm. The separation between the slits is \[2 \cdot 0 \times {10}^{- 3}m.\]
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Solution
Given
Wavelength of the blue-green light,
\[\lambda = 500 \times {10}^{- 9} m\]
Separation between two slits,
\[d = 2 \times {10}^{- 3} m,\]
Let angular separation between the consecutive bright fringes be θ.
Using \[\theta = \frac{\beta}{D} = \frac{\lambda D}{dD} = \frac{\lambda}{d},\] we get
\[ \theta = \frac{500 \times {10}^{- 9}}{2 \times {10}^{- 3}}\]
\[ = 250 \times {10}^{- 6} \]
\[ = 25 \times {10}^{- 5}\text{ radian or }0.014^\circ\]
Hence, the angular separation between the consecutive bright fringes is 0.014 degree.
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