Question

A pair of narrow, parallel slits separated by 0.220 mm is illuminated by green light (λ = 546.1 nm). The interference pattern is observed on a screen 1.50 m away from the plane of the parallel slits.

(a) Calculate the distance from the central maximum to the first bright region on either side of the central maximum.
  ____mm

(b) Calculate the distance between the first and second dark bands in the interference pattern.
  ____mm

Answer 1

The equation for the distance between the first maxima and central is

\(\frac{y}{L}=\frac{m \lambda}{d}\)

$$ y_{2}-y_{1}=\frac{\left(m_{2}-m_{1}\right) \lambda}{d} L $$

\(\Delta y=\frac{(1) 546.1 \times 10^{-9}}{\left(0.22 \times 10^{-3}\right)}(1.5)=3.72 \mathrm{~mm}\)

b)

Distance between the first and second dark band is

$$ y_{2}-y_{1}=\frac{\left[\left(m_{2}+\frac{1}{2}\right)-\left(m_{1}+\frac{1}{2}\right)\right] \lambda}{d} L $$

\(y_{2}-y_{1}=\frac{\left[\left(1+\frac{1}{2}\right)-\left(0+\frac{1}{2}\right)\right] \lambda}{d} L\)

\(\Delta y=\frac{(1) 546.1 \times 10^{-9}}{\left(0.22 \times 10^{-3}\right)}(1.5)=3.72 \mathrm{~mm}\)