Question

Visible light passes through a diffraction grating that has 900 slits per centimeter, and the interference pattern is observed on a screen that is 2.80m from the grating. In the first-order spectrum, maxima for two different wavelengths are separated on the screen by 3.10mm . What is the difference between these wavelengths? in meters

Answer 1

No.of slits per cm is  = 900

No.of slits per m is N = 90000

Grating element d = 1 / N = 1.1111 * 10 ^ -5 m
distance of the scrren from grating D = 2.8 m

For 1 st order d sin ? = ?

from samll angles   d ( y / D ) = ?

                                   y = ?D / d   ----( 1)

for another wavelength ? ' :

---------------------------

d sin ?' = ? '

from samll angles   d ( y ' / D ) =?'

                                   y ' = ?' D / d   ----( 2)

given y ' - y = 3.1 mm = 3.1 * 10 ^ -3 m

( ?' D / d ) - ( ? D / d ) = 3.1 * 10 ^ -3m

   ( ?' - ? ) ( D / d ) = 3.1 * 10 ^ -3m

from this wavelength diffeence ? ' - ? = ( 3.1* 10 ^ -3 ) d / D

= ( 3.1* 10 ^ -3 )(1.1111 * 10 ^ -5) / 2.8

                                                         = 1.2301 * 10 ^ -8 m = 12.3 nm