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Find the wavelength of the light used to produce a double slit diffraction pattern where the...

Find the wavelength of the light used to produce a double slit diffraction pattern where the second order image is 0.035 m from the central image using a diffraction grating constant of 5.2 x 10-5 m. The screen is located 2.0 m from the slits.

Can you show this using the small angle approximation formula please?

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Answer #1

For a double slit experiment , the formula for bandwidth is

=

where

is the wavelength

D is the distance of the screen from the slits

and d is the distance between slits.

but I think the distance between the slits d is mistakenly given as grating constant. because grating constant is the reciprocal of d. so as per the given value of grating constant, the distance between the slits will be a very great value , which is not possible.

so d= 5.2 X 10-2 m

D = 2m

so,

= 0.0175 X 5.2 X 10-5 /2

= 4.55 X 10-7 m

= 455 nm (ans)

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