Question

A digital video disc records information in a spiral track about $1 \mu \mathrm{m}$ wide. The track consists of a series of pits in the information layer (see Fig. P25.20a) that scatter light from a laser beam sharply focused on them. The laser shines in through transparent plastic of thickness $t=1.20 \mathrm{mm}$ and index of refraction $1.55 .$ Assume that the width of the laser beam at the information layer must be $a=1.00 \mu \mathrm{m}$ to read from just one track and not from its neighbors (Fig. P25.20b). Assume that the width of the beam as it enters the transparent plastic from below is $w=0.700 \mathrm{mm} .$ A lens makes the beam converge into a cone with an apex angle $2 \theta_{1}$ before it enters the disk. Find the incidence angle $\theta_{1}$ of the light at the edge of the conical beam. Note that this design is relatively immune to small dust particles degrading the video quality. Particles on the plastic surface would have to be as large as $0.7 \mathrm{mm}$ to obscure the beam.

          A digital video disc records information in a spiral track about $1 \mu \mathrm{m}$ wide. The track consists of a series of pits in the information layer (see Fig. P25.20a) that scatter light from a laser beam sharply focused on them. The laser shines in through transparent plastic of thickness $t=1.20 \mathrm{mm}$ and index of refraction $1.55 .$ Assume that the width of the laser beam at the information layer must be $a=1.00 \mu \mathrm{m}$ to read from just one track and not from its neighbors (Fig. P25.20b). Assume that the width of the beam as it enters the transparent plastic from below is $w=0.700 \mathrm{mm} .$ A lens makes the beam converge into a cone with an apex angle $2 \theta_{1}$ before it enters the disk. Find the incidence angle $\theta_{1}$ of the light at the edge of the conical beam. Note that this design is relatively immune to small dust particles degrading the video quality. Particles on the plastic surface would have to be as large as $0.7 \mathrm{mm}$ to obscure the beam.

Added by John N.

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