Here is the problem:(adsbygoogle = window.adsbygoogle || []).push({});

A glass sphere with a diameter of 5cm has a scratch on its surface. When the scratch is viewed through the glass from a position directly opposite, where is the virtual image of the scratch, and its magnification? The glass has an index of refraction n=1.50. Explain the result.

[Answer: s'=-10cm; 3x]

I've constructed a system of matrices that looks like this:

M_{3}*M_{2}*M_{1}

M_{1}is for the first refraction of the scratch at the sphere's front surface.

M_{2}is for the translation of the ray through the glass.

M_{3}is for the second refraction through the second surface of the glass where the viewer is located.

When I multiply the matrices together I get these equations.

y_{f}=-2/3y_{o}+ 10/3α_{o}

α_{f}=-4/15y_{o}+ 1/3α_{o}

I do not understand how I use the geometry of the ray to locate an image of a scratch. What am I missing in all of this? Did I use the matrix equation properly? What do I do, I'm extremely stumped?

Thanks for any help.

Frank

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# Ray tracing with matrices

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