p37_007 - 7. The condition for a minimum of intensity in a...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 7. The condition for a minimum of intensity in a single-slit diffraction pattern is a sin θ = mλ, where a is the slit width, λ is the wavelength, and m is an integer. To find the angular position of the first minimum to one side of the central maximum, we set m = 1: θ1 = sin−1 λ a = sin−1 589 × 10−9 m 1.00 × 10−3 m = 5.89 × 10−4 rad . If D is the distance from the slit to the screen, the distance on the screen from the center of the pattern to the minimum is y1 = D tan θ1 = (3.00 m) tan(5.89 × 10−4 rad) = 1.767 × 10−3 m . To find the second minimum, we set m = 2: θ2 = sin−1 2(589 × 10−9 m) 1.00 × 10−3 m = 1.178 × 10−3 rad . The distance from the center of the pattern to this second minimum is y2 = D tan θ2 = (3.00 m) tan(1.178× 10−3 rad) = 3.534 × 10−3 m. The separation of the two minima is ∆y = y2 − y1 = 3.534 mm − 1.767 mm = 1.77 mm. ...
View Full Document

Ask a homework question - tutors are online