A laser with wavelength 56.25 mu m is shining light on a double slit with slit s

Question

A laser with wavelength 56.25 mu m is shining light on a double slit with slit separation 0.450 mm. This results in an interference pattern on a screen a distance L away from the slits. We wish to shine a second laser, with a different wavelength, through the same slits such that the fourth minimum of the first laser is at the same location as the second maximum of the second laser. What is the wavelength lambda_2 of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser, if d = 0.450 mm? Express your answer in micrometers using three significant figures..

Explanation / Answer

condition for diffraction maximum is

d sin theta = m lamda2

condition for diffraction minimum

d sin theta = ( m- 1/2) lamda1

for fourth minimum

d sin theta = ( 4- 1/2) lamda 1

for second maximum

d sin thet a= 2 lamda 2

( 4- 1/2) lamda 1= 2 lamda 2

lamda 2 = 3.5 lamda 1/2

=3.5( 56.25 um)/2

=98.43 um

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