After reaching a distant planet, an astronaut on your ship is scanned by the ali

Question

After reaching a distant planet, an astronaut on your ship is scanned by the alien life forms using a polarized light source. Polarized light passing through a medium with absorbed sugar will experience a net rotation due to an asymmetry in the shape of the sugar molecules. Assume the net effect on the incident polarization when testing a human after fasting is negligible. The scanning machine (polarimeter) measures a 0.15 degree rotation per cm of human after one donut is consumed. Assume the intensity of the light is otherwise unaffected as it shines through our subject, because this can be corrected by a calibration measurement. When the aliens test their subject, the measured light intensity of the transmitted beam is found to be 17.3% of the light intensity incident on the astronaut. How many donuts did our astronaut consume?

Include work please.

Explanation / Answer

We know that

From the Malus law

I =Iocos2theta

Given that theta =0.15degrees

Then I =(0.999993)Io

The change in intensity is DeltaI =Io-I =6.85*10-6*Io

Now the change in final intensity is DeltaIfinal =(100-17.3)% of Io =(82.7/100)Io =0.827Io

The change in final intensity (DeltaIfinal) =n*DeltaI

Then the number of donuts did our astronaut consume is n=0.827Io/6.85*10-6*Io =1.207*105donuts

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