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White light is passed through a double slit and interference pattern is observed on a screen 2.5 m away. The separation between the slits is 0.5 mm. The first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringe. Calculate the wavelengths of the violet and the red light.

Text Solution

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for the first bright fringe, the distasnce from the centre is
`y=(Dlamda)/d`
for violet light `y=2.0. Thus,
`2.0 mm=((2.5m)lamda)/(0.5mm)`
`or lamda=((0.5mm)(2.0mm))/(2.5mm)=400nm`
`Similarly for red light, y=3.5 mm. thus,
`3.5mm=((2.5m)lamda)/(0.5mm)`
`or lamda=700nm`
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