39. (a) The angular positions θof the bright interference fringes are given by dsin = mλ, where dis the slit separation, λis the wavelength, and mis an integer. The first diffraction minimum occurs at the angle 1given by asin 1= λ, where ais the slit width. The diffraction peak extends from –1to +1, so we should count the number of values of mfor which –1< < +1, or, equivalently, the number of values of mfor which – sin 1< sin < + sin 1. This means – 1/a < m/d< 1/aor –d/a < m < +d/a. Now d/a= (0.150 ×10–3m)/(30.0 ×10–6m) = 5.00, so the values of mare m= –4, –3, –2, –1, 0, +1, +2, +3, and +4. There are 9 fringes.
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.