Question 217: Waves Optics

Question

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by 5 $$	imes$$ 10$$-$$2 m towards the slits, the change in fringe width is 3 $$	imes$$ 10$$-$$3 cm. If the distance between the slits is 1 mm, then the wavelength of the light will be ____________ nm.

Accepted Answer

Fringe width $$\beta  = {{\lambda D} \over d}$$
$$ \Rightarrow \left| {d\beta } ight| = {\lambda  \over d}\left| {d(D)} ight|$$
$$ \Rightarrow 3 	imes {10^{ - 3}}\,cm = {\lambda  \over {1\,mm}}\left( {5 	imes {{10}^{ - 2}}\,m} ight)$$
$$ \Rightarrow \lambda  = {{3 	imes {{10}^{ - 8}}} \over {5 	imes {{10}^{ - 2}}}}\,m$$
$$ \Rightarrow \lambda  = 600\,nm$$

Waves Optics

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