Question

Two thin parallel slits that are 1.08×10−2 mm apart are illuminated by a laser beam of wavelength 590 nm . Part A On a very large distant screen, what is the total number of bright fringes (those indicating complete constructive interference), including the central fringe and those on both sides of it? Solve this problem without calculating all the angles! (Hint: What is the largest that sinθ can be? What does this tell you is the largest value of m?)

Answer 1

37 fringes

Step-by-step explanation:

To find the values of the maxima number of fringes you use the following formula for the condition for constructive interference:

`m\lambda=dsin\theta\\\\`

λ: wavelength

d: distance between slits

Furthermore, you use the fact that the maximum order m of the fringes is obtain for an angle of 90°, that is:

`m=(dsin\theta)/(\lambda)\\\\m_(max)=(d)/(\lambda)`

you replace the values of the parameters to obtain the maximum order:

`m_(max)=(1.08*10^(-2)*10^(-3))/(590*10^(-9)m)=18.3\approx18`

that is, there are 18 fringes above the central maximum, the total fringes will be twice this value plus the central maximum

Total fringes = 2*18+1=37 fringes