How Close Can You Get to a 720p TV Before Seeing Individual Lines?

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Homework Help Overview

The discussion revolves around determining the minimum viewing distance from a 720p television before individual horizontal lines become visible. The problem involves concepts from optics and diffraction, specifically Rayleigh's Criterion, and applies to a scenario with a specific screen size and light wavelength.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the application of Rayleigh's Criterion to calculate the minimum viewing distance. Questions arise regarding the correct use of parameters, such as the separation of horizontal lines and the diffraction coefficient.

Discussion Status

The discussion is ongoing, with participants providing feedback on each other's calculations and questioning the assumptions made, particularly regarding the diffraction coefficient and the parameters used in the calculations. There is no explicit consensus yet, but several lines of reasoning are being explored.

Contextual Notes

Participants are working with specific values, such as the height of the screen and the number of horizontal lines, while also considering the medium in which the diffraction pattern is observed. There is an emphasis on ensuring the correct interpretation of the problem's parameters.

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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!
 
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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.
 
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...
 
Are you sure about that diffraction coefficient you are using? Perhaps it is not necessary.
 
I believe so. In the book it says to take into account in which medium the diffraction pattern is observed.
 

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