Question

Laser of wavelength 670 nm passes through a slit of width 0.08 mm. The diffraction pattern is formed on a distant screen. What is the angle of the farthest dark fringe from the central line?

a. 86.7o

b. 85.3o

c. 83.5o

d. 87.6o

Answer 1

answer) first we have to find the maximum number of dark fringes

we have the formula

dsin$\Theta$=m$\lambda$

for interference to occur the angle $\Theta$ should be less than 90^o

which means sin$\Theta$>1

so we have

sin$\Theta$=m$\lambda$/d......1)

m$\lambda$/d>1

m>d/$\lambda$

m>8*10^-5m/670*10^-9

m>119

so m=119

so using eqn 1

so $\Theta$=sin^-1( 119*670*10^-9/8*10^-5)

$\Theta$=85.3⁰

so the correct option is b) 85.3^o.