Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Introductory Physics Homework Help
Single-slit Diffraction Problem
Reply to thread
Message
[QUOTE="lingualatina, post: 5820649, member: 449743"] [h2]Homework Statement [/h2] A spy camera is said to be able to read the numbers on a car’s license plate. If the numbers on the plate are 5.0 cm apart, and the spy satellite is at an altitude of 160 km, what must be the diameter of the camera’s aperture? (Assume light with a wavelength of 550 nm.) [h2]Homework Equations[/h2] Single-slit diffraction: [I]w[/I]sin[I]θ[/I] = [I]mλ[/I] (where [I]w[/I] is the width of the slit, [I]m[/I] = 1, 2, 3, ... for destructive interference) Small-angle approximation: sin[I]θ[/I] ≈ tan[I]θ[/I] = [I]y[/I]/[I]D[/I] (where [I]y[/I] is the vertical height above the central axis, [I]D[/I] is the distance between the slit(s) and the screen) for small [I]θ[/I] [h2]The Attempt at a Solution[/h2] Since the goal of the problem is to solve for [I]w[/I], I used the small-angle approximation to set up the following equation: [I]mλ[/I]/[I]w[/I] = [I]y[/I]/[I]D[/I]. I then rearranged the variables to isolate [I]w[/I], ending up with [I]w[/I] = [I]mλy[/I]/[I]D[/I]. Now, I know that [I]D[/I] = 160 * 10[SUP]3[/SUP] m and λ [I]= [/I]500 * 10[SUP]-9[/SUP] m. I'm having trouble, however, figuring out what to do for [I]m[/I] and [I]y[/I]. Since the numbers on the plate are 5.0 cm apart, I'm assuming that, every 5.0 cm, we have constructive interference occurring. Since there will definitely be constructive interference along the central axis, I figured that the first-order minimum would occur halfway in-between the central bright fringe and the first-order bright fringe, which would give [I]m[/I] = 1 and [I]y[/I] = 2.5 cm. However, this does not give me the correct answer; if I try instead to use [I]m[/I] = 1 and [I]y [/I]= 5.0 cm, this [I]does[/I] give me the right answer, but I can't come up with a sketch of the situation that would explain why. Some assistance with the intuition here would really be appreciated. Thank you very much in advance for your help! [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Introductory Physics Homework Help
Single-slit Diffraction Problem
Back
Top