Physic help please thank you?

Question

A laser beam with wavelength 650nm illuminates a narrow slit. The diffraction pattern of the slit is projected on a screen 2.5 m from the slit. The width of the central maximum is measured to be 6.0 mm.

I used this equation: y= m ( λL/ a)

A. The distance from the first dark fringe to the center of the diffraction patter on the screen is...the answer given was 3.0 mm ( i dont know how they get that answer)

B. the width of the slit is....answer given was 0.542 mm ( i dont know how to get this answer either)

Answer 1

A. The central band which is a bright fringe has a width of 6.0 mm. To measure this bright fringe, you effectively measure the distance between first dark fringes on either side of the central.

So you divide 6 mm by 2 to get 3 mm, the answer.

B. Sub y = 3e-3 m, λ = 650e-9, L = 2.5 m, m = 1 to your equation

a = 0.000542 m = 0.542 mm