# In terms of d and n 0 d min 2 sin n 2 has

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: of λ, d and N). 0 θmin λ/d θ Lecture 4, p 6 Solution In an N-slit interference pattern, at what angle θmin does the intensity first go to zero? (In terms of λ, d and N). 0 λ/d θmin θ 2 ⎛ྎ sin( Nφ / 2) ⎞ྏ has a zero when the numerator is zero. That is, φmin = 2π/N. I N = I1 ⎜ྎ ⎟ྏ sin(φ / 2) ⎠ྏ Exception: When the denominator is also zero. ⎝ྎ That’s why there are only N-1 zeros. But φmin = 2π(d sinθmin)/λ ≈ 2πd θmin/λ = 2π/N. Therefore, θmin ≈ λ/Nd. As the number of illuminated slits increases, the peak widths decrease! General feature: Wider slit features à༎ narrower patterns Narrower slit features à༎ wider patterns.... Lecture 4, p 7 Note:The simple calculations we have done only hold in the “far-field” (a.k.a. “Fraunhofer” limit), where L >> d2/λ. Intermediate cases (“Fresnel diffraction”) can be much more complex… Interference Gratings Examples around us. CD disk – grooves spaced by ~wavelength of visible light. The color of s...
View Full Document

Ask a homework question - tutors are online