A compact disc (CD) is read from the bottom by a semiconductor laser with wavele

Question

A compact disc (CD) is read from the bottom by a semiconductor laser with wavelength 790 nm passing through a plastic substrate of refractive index 1.8. When the beam encounters a pit, part of the beam is reflected from the pit and part from the flat region between the pits, so these two beams interfere with each other (see figure below). What must the minimum pit depth be so that the part of the beam reflected from a pit cancels the part of the beam reflected from the flat region? (It is this cancellation that allows the player to recognize the beginning and end of a pit. For a fuller explanation of the physics behind CD technology, see the article "The Compact Disc Digital Audio System," by Thomas D. Rossing, in the December 1987 issue of The Physics Teacher.) ? µm

Explanation / Answer

For the beams to cancel the gap must be a quarter wavelength because in order , there must be a phase change of 1/2 wavelength. If the gap is a quarter wavelength then the second beam travels 1/4 down and 1/4 back up, making the overall distance traveled 1/2 wavelength longer.

1/4 of 790 is 197.5 nm, taking wavelength being shortened by the refractive index in account.

197.5 / 1.8 = 109.72 nm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.