A diffraction grating formed by parallel adjacent tracks on a CDROM

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Start date Mar 23, 2020
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Diffraction Diffraction grating Grating Parallel

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The discussion centers on the calculation of the grating spacing (d) for a diffraction grating formed by parallel tracks on a CD-ROM. The derived value of d is 730 nm, based on the equation (d)sin(40.6)=(475*10^-9)(1). However, a professor asserts that the correct answer should be 1460 nm, indicating a discrepancy in the expected values for CD and DVD track separations, which are typically 1.6 micrometers and 740 nm, respectively.

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Understanding of diffraction principles and equations
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Knowledge of CD and DVD technology specifications
Basic mathematical skills for solving trigonometric equations

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Mar 23, 2020

help I have 12 hours

Homework Statement: The parallel tracks on a CD-ROM reflect light just like a diffraction grating. Looking at a CD-ROM under white light, you observe a bright reflection of 475 nm blue light at 40.6° from normal incidence. The next bright blue reflection occurs at 77.2°.

Calculate the spacing between the CD-ROM tracks. Show your work here, and then enter your final numeric answer in the next answer box.

Relevant Equations: (d) sin(theta)=(wave length)*m

(d)sin(40.6)=(475*10^-9)(1)

d=730*10^-9 (m)

prof says answer is 1460*10^-9 (m) tho

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Mar 23, 2020

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I agree with your answer but something is weird in general. The 77.2 degree don't fit to the next band. 1.6 micrometers is the usual separation for a CD. 740 nm for a DVD.