This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Physics 208, Assignment 9, Solutions, 3/30/09, RT Problem 1. The figure shows a conjectured reflection for which, in order to set up equations, the outgoing angle is visibly different from the incoming angle . By definition of a wavefront the incident rays labeled 1 2 x cos x cos 1 2 G F x F G 1 and 2 are in phase at the points F and G, points on the same wavefront. According to Huyghens, when the outgoing rays 1 and 2 are viewed in the distance (or, as one says, at infinity) they will add constructively if they are in phase at the points F and G. This will be true if the distances GG and FF are equal, or x cos = x cos , or = . (1) Strictly speaking we also have to prove an only if statement as well. Eq. (1) is also satisfied when distances GG and FF differ by an inte gral number of wavelengths. This can happen for various discrete values of x . But, for constructive interference of all rays on the wavefront FG requires Eq. (1) to be satisfied for all values of x . So there is reflection if and only if = . This reflection is referred to as specular which, I think, means, the same for all colors. The argument above showing independence from x can be rephrased to prove independence of wavelength . 1 Problem 2. The problem states that two slits are separated by 25 wave lengths. It would not be wrong to work in units of length such that the wavelength is 1 unit. But that might be confusing. Hence we introducewavelength is 1 unit....
View
Full
Document
 Spring '08
 AMADEURI
 Physics

Click to edit the document details