Question

How many dark fringes will be produced on either side of the central maximum if light ( = 682 nm) is incident on a single slit that is 5.11 × 10-6 m wide?

Answer 1

From dark fringe equation:

sin(theta) = m*lambda/width

lambda = 682*10^-9 m

width, w = 5.11*10^-6 m

lambda/width =  682*10^-9 m /  5.11*10^-6 m = 0.1335

since, sine(theta) must be less than or equal to 1,

therefore, we need a number that when multiplied by 0.1335 will be less than or equal to 1

10*0.1335 = 1.335 > 1

so, 9*0.1335 = 1.2015 > 1

8*0.1335 = 1.068 > 1

7*0.1335 = 0.9345 < 1

Therefore, the number of fringes is 7 (Seven).