The paint used on highway signs often contains small transparent spheres which p

Question

The paint used on highway signs often contains small transparent spheres which provide nighttime illumination of the sign's lettering by retro-reflecting vehicle headlight beams. Consider a light ray from air incident on one such sphere of radius r and index of refraction n. Let ? be its incident angle, and let the ray follow the path shown in the figure, so that the ray exits the sphere in the direction exactly antiparallel to its incoming direction. Considering only rays for which

sin? can be approximated as ?, determine the required value for n

The paint used on highway signs often contains small transparent spheres which provide nighttime illumination of the sign's lettering by retro-reflecting vehicle headlight beams. Consider a light ray from air incident on one such sphere of radius r and index of refraction n. Let ? be its incident angle, and let the ray follow the path shown in the figure, so that the ray exits the sphere in the direction exactly antiparallel to its incoming direction. Considering only rays for which can be approximated as ?, determine the required value for n

Explanation / Answer

for it to happen, angle of refraction should be theta/2.

So, n = sin (theta) / sin(theta/2)

= theta/theta/2

= 2

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