How Is Path Length Difference Calculated in a Two-Slit Interference Pattern?

[msusparty1136]

Homework Statement

Two slits separated by a distance of d = 0.115 mm are located at a distance of D = 2.43 m from a screen. The screen is oriented parallel to the plane of the slits. The slits are illuminated by a monochromatic and coherent light source with a wavelength of λ = 595 nm. A wave from each slit propagates to the screen. The interference pattern shows a peak at the center of the screen (m=0) and then alternating minima and maxima. What is the path length difference between the waves at the first maximum (m=1) on the screen? At what angle from the beam axis will the first (m=1) maximum appear? (You can safely use the small angle approximation.)

Homework Equations

The Attempt at a Solution

 

[WatermelonPig]

Assume the rays from the slits are effectively parralell. A maximum occurs when the path length difference is a multiple of the wavelength because this is constructive interference. The path length difference is dsin(theta) which for constructive interference is equal to m(lamda).