- #36

Not anonymous

- 143

- 58

Thanks for reviewing the answer. (Eq. 1) in the solution I gave is already an expression involving only ##a, d, \Delta y##, so I am not sure I understand what is meant by simplifying to ##\lambda (a,d,\Delta y)##. Do you mean a simpler expression that does not involve difference of square roots? I couldn't get any satisfactory simplification by extracting ##a## out of the square root expressions, but I will try again tomorrow.fresh_42 said:Can you simplify this to ##\lambda =\lambda (a,d,\Delta y)## under the assumption ##a \gg d ## and that the beams that run from ##A## and ##B## in direction ##P## on the screen are approximately parallel? And where did you use the interference pattern?

I am using the interference pattern to derive the difference between the lengths traveled by the 2 rays to reach Q'. The central bright fringe is equidistant from A and B and so the 2 rays interfering there will be in exactly the same phase, i.e. the 2 waves reaching and positively interfering at Q' at any instant ##t_1## would have originated from the 2 images at the same instant ##t_0##, and hence the same number of waves would have been emitted along the 2 paths. In case of the next bright fringe (in the solution, I considered the one immediately above the central fringe, but the same applies to the first bright fringe below too), the 2 constructively interfering waves would differ in phase by 1 wavelength, i.e. they would have originated from the sources at time instants that are ##\dfrac{1}{f}## seconds apart, where ##f = \dfrac{c}{\lambda}## is the frequency of the emitted light (assuming that it is okay to ignore the minor variations in speed of light as it passes through prism and non-vacuum air). In general, if we consider the bright fringe that is ##n## fringes above or below the central bright fringe, the waves interfering there would different in phase by ##n## times the wavelength, i.e. they would have been emitted from the source ##\dfrac{n}{f}## seconds apart. Am I missing something?