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.) mu m

Explanation / Answer

The gap must be a quarter wavelength

because in order for the beams to cancel, you must have 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 total distance travelled 1/2 wavelength longer.
given wavelength =790nm
(1/4 )x790 = 197.5nm

, but then you need to take into account the wavelength being shortened by the refractive index.

Refractive index n=1.8

=197.5 / 1.8 = 109.72 nm

=0.10972 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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