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Show the steps to arrive at eqn 3 from eqn 1.  Eqn 1: d sinθ = m λ Eqn 3: yd/L=m λ

Show the steps to arrive at eqn 3 from eqn 1.  Eqn 1: d sinθ = m λ Eqn 3: yd/L=m λ

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Show the steps to arrive at eqn 3 from eqn 1. 

Eqn 1: d sinθ = m λ

Eqn 3: yd/L=m λ

Further approximation: In two-slit, we often only care to look at spots reasonably close to the center of the screen (i.e. "small" values of 0). Since this is the case, we can make one more useful approximation in addition to the above. This is called the small angle approximation, one of whose consequences is that sin 0 = tan 0. Examining Fig 1, one can find that tan 0 = y/L. Substituting that in for sin 0 in eqn 1 gives (see Q4). yd Am (3) Since eqns 1-2 are the same except the role of 'd' is replaced by W' , it is trivial to form the single slit version of eqn 3.
Transcribed Image Text:Further approximation: In two-slit, we often only care to look at spots reasonably close to the center of the screen (i.e. "small" values of 0). Since this is the case, we can make one more useful approximation in addition to the above. This is called the small angle approximation, one of whose consequences is that sin 0 = tan 0. Examining Fig 1, one can find that tan 0 = y/L. Substituting that in for sin 0 in eqn 1 gives (see Q4). yd Am (3) Since eqns 1-2 are the same except the role of 'd' is replaced by W' , it is trivial to form the single slit version of eqn 3.
Maxima locations (two-slit): d sin 0 = m. (1) m = 0, ±1, ±2... = maxima spots away from the central maxima (m=0) 1 = wavelength of light projected on the double slits. d %3D distance between the two slits (center to center). 0 = angle on the observation screen we are looking (center of screen is 0 =0)
Transcribed Image Text:Maxima locations (two-slit): d sin 0 = m. (1) m = 0, ±1, ±2... = maxima spots away from the central maxima (m=0) 1 = wavelength of light projected on the double slits. d %3D distance between the two slits (center to center). 0 = angle on the observation screen we are looking (center of screen is 0 =0)
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