Given a block of glass that is semi-circular, a laser pointer, protractor/ruler,

Question

Given a block of glass that is semi-circular, a laser pointer, protractor/ruler, and index card, design your own experiment to observe and measure total internal reflection. Describe how you would shine the laser onto the glass block, what angles you would measure and how you would determine the critical angle from your measurements.

Draw the block of glass and the bean going through it at the critical angle. Show where total internal reflection occurs. (assume sample is n=1.52) Draw this angle and all other values and all others as accurately as you can. Label the critical angle and give its value. Remember total internal reflection occurs only when light goes from a denser medium (sample) into one of lower index (air n=1).

Please be as thorough with you explaination was you can.

Explanation / Answer

Start from snell's law....Ni X sin Ai = Nr x sin Ar

for total internal reflection in your case Nr =1 Ni = 1.52 , sin Ar =1 as limit for crtical angle.
so, 1.52 x sin Ai =1
so, sin Ai = 1/1.52 = 41.14 deg.
ie beam comes at 41.14 deg to normal in glass ( ie radius ), if coming out of curved side then at 48.86 deg to the curved edge surface/ tanget .
it is cumbersome to solve for min/max angle of incidence into the glass from air and you need proroctracter ruler to trace back the point of entrance into glass from any edge of the semicircular disc, so that the point of total internal reflection lies on the curved surface. always keep inj mind to bend the drawn rays as per ref. index at point of entrance.

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