Question

What is the distance \\(x_n-x_m\\) between the \\(n\\)-th bright fringe and the \\(m\\)-th dark fringe?

Options

• \\[x_n-x_m=\\left[n+\\frac{2m-1}{2}\\right]\\beta\\]

• \\[x_n-x_m=\\frac{n\\beta}{2m-1}\\]

• \\[x_n-x_m=\\left[n-\\frac{2m-1}{2}\\right]\\beta\\]

• \\[x_n-x_m=(n-m)\\beta\\]

Answer 1

A bright fringe is at \\(x_n=n\\beta\\), while a dark fringe is at \\(x_m=(2m-1)\\beta/2\\). Subtracting their positions gives the stated expression.