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Optics: Resolution Problem

  • Thread starter kmj9k
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  • #1
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1. The American Television Systems Committee (ATSC) sets the standards for high-definition television (HDTV). One of the approved HDTV formats is 720p, which means 720 horizontal lines scanned progressively - one line after another in sequence. Suppose the 720 lines are displayed on a television with a screen that is 28 inches high, and that the light coming from the screen has a wavelength of 505 nm. If the pupils of your eyes have a diameter of 5.5 mm, what is the closest you can be to the TV before seeing the individual horizontal lines? (This is the minimum acceptable viewing distance.)


2. Rayleigh''s Criterion: theta min = 1.22 (lambda/D); L = (y/ (tan theta min))




3. To find theta min, I did 1.22 ((505*10^-9)/1.36)/0.0055) and got 8.237 * 10^-5 rad. I divided the wavelength by 1.36 since that is the index of diffraction for the eye. Then, I plugged it into the L = equation: L= 0.7112 m /tan (8.237*10^-5) and got a final answer of 8634, which is incorrect.

Where did I go wrong? Thank you!
 

Answers and Replies

  • #2
hage567
Homework Helper
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I don't think you should be using y = 0.7112 m. You want to find the separation of two of the horizontal lines, which you can figure out because you know how many lines are in the 28" screen.
 
  • #3
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I tried dividing 0.7112 m by 720 and got 9.8778e-4. I then plugged that into the L = y/ (tan theta min)) and got 11.99, which is still incorrect...
 
  • #4
hage567
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Are you sure about that diffraction coefficient you are using? Perhaps it is not necessary.
 
  • #5
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I believe so. In the book it says to take into account in which medium the diffraction pattern is observed.
 

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