Question

A laser with wavelength d/8 is shining light on a double slit with slit separation 0.400mm . 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.

A) What is the wavelength ?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 = 0.400mm ?

Express your answer in millimeters.

?2 = ------------ mm

Answer 1

In interfreence or diffraction pattern
the needed equation is Y = mLR/d---------------1
and d sin theta = mL--------------------2
where L = wavelgnth
m = order = 1,2,3,4, ......... for brigth bands
m = 1.5, 2.5, 3.5, 4.5, ......for dark bands
R is the distance from slit to screen
Y = disatnce from central spot to nth order fringe or fringe width
so here now we applyapply Y = mLR/d

Y = 3.5 * d/8 * R/ 0.4mm

Y/R = 0.4375

now Y2 = mL2R/d

L2 = Y(0.4mm)/mR

L2 = 0.4375 *0.4mm/2

L2 = 0.0875 mm