A DVD is a video recording consisting of a spiral track about 1.0 mu m wide with

Question

A DVD is a video recording consisting of a spiral track about 1.0 mu m wide with digital information. The digital information consists of a series of pits that are read by a laser beam sharply focused on a track in the information layer. If the width "a" of the beam at the information layer must equal 1.0 mu m to distinguish individual tracks and the width "w" of the beam as it enters the plastic is 0.7 mm, find the angle theta 1 at which the conical beam should enter the plastic. The plastic has a thickness of t = 1.2 mm and an index of refraction of n = 1.55. See Picture.

Explanation / Answer

split the drawing in half, lengthwise. Then you have a triangle with

long side t = 1.2 mm

short side b = (w-a)/2 = (0.700 - 0.001)/2 = 0.6995 mm

so

angle @2 = arctan(short side / long side) = arctan(0.6995/1.2) =

= 30.2386 degrees

then using refraction

1.55 sin30.2386 = 1.00 sin@1

@1 = 51.31 degrees

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