Question

24.23: When blue light of wavelength 470 nm falls on a single slit, the first dark bands on either side of center are separated by 55.0 ∘. A) Determine the width of the slit.

Answer 1

Equation: dsinθ = mλ

It is basic plug and chug from here because you know the wavelength, you know the angle and the m=1 since it's beside the center fringe which is m=0. The tricky part is the angle which needs be halved because we are only concerned with the angle between m=1 and m=0 and they gave you the angle between m=1 to the right of the center and m=1 on the left of the center.

so...

dsin(55/2)=(1)(470)

=> d = 470nm/sin(55/2)

= 1017.9 nm

or 1.0179 x 10^-6 m