class25lecnotes

# class25lecnotes - -thIs is'Sn~ll-ia;hich tells us that...

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-- thIs is 'Sn~ll' ;-ia;:;hich tells us that light bends when it moves from one medium with a given index of refraction into a medium with a larger index of refraction. In this context, we briefly describe the procedure through which w~ analyze refraction. I ~ ~r I ~ ~ ~ "'" ~ " \'\J I"- ~, N ~ 1\. i'f'l 'S ~l ' "" \ .... 1. Represent the light beam with one ray. ~ ...... 2. Draw. the perpendicular to the interface at the point where the ray hits the , I interface. Label the angle ofineidenee'Ol (with respect to the perpendicular!). 3. Show how this incident ray is bent upon passing beyond the interface, labeling the 'I ~ angle of refraction O 2 (again with respect to the perpendicular). " 4. Repeat the procedure, if there is more, than one interface. ~. 5. Use Snell's Law to compute the index of refraction. .... ~ ): ;,;::

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----- (/Jd . .r) Example 1. A laser beam is aimed at a lcm thick sheet of glass at an angle of 30 0 above the glass surface. A) What is the beam's direction of travel in the glass? B) What is its direction in the air on the other side of the glass? C) By what distance is the beam displaced with respect to its original direction? tt _ 2 Vz.- . (I, ~ riu &, ~ I?, f/11 &z j = ) .u.;.. ~ ~ 1?'.\$iM. ~ /?, - I I flz. - n ~ __ "':::";'--"-_~ ___ _ t<r.l(}.M 11= I.S I = > '..1 AM 6t2°__ VI fi .) fin (7l. .: - - =_ c. () . .J9 I . .r z·!) 1 :.;> L &,. ~ s r: 1 j t} &3; e z 4 ~~ :: ~ ) I'1us WI4 /./dl'UI dul ~ ~ (a-til) 611-ac tiolJ-JJ.]~,:: < 1: ;I 0 1=111 C .: ~-4 /MAti /J ,48b: ;) 1M:: /)f) tl:JtJi Being able to write down Snell's Law, and solving problems based on it does not, however, mean that we understand refraction. Snell's Law tells us how light bends. It does not tell us why it bends. We can provide a somewhat deeper answer in terms of the Least-Time Principle: It bends in order to minimize the travel time between two given points on either side of the refracting surface. Light has to shorten its path through a medium with a larger index of refraction because through that medium it moves at a lower speed. We have long guessed that the index of refraction must have something to do with the ratio of the speeds of light through the two media: {n:; Clv]
This connection was not clear at the time Snell worked out his law. Light is an electromagnetic wave, which has the special property of being able to propagate through nothing (vacuum). This is possible, so we learned, because the electric and magnetic fields that oscillate in an electromagnetic wave can regenerate each other. A changing electric field enforces a changing magnetic field through a process called induction, and vice versa. All electromagnetic waves travel at the speed of light. When an electromagnetic wave reaches a medium, e.g our atmosphere, windows, etc., these oscillating electric fields are forcing charged particles within the material to respond to the oscillation and accelerate back and forth with it. This periodic acceleration gives rise to a new source of changing electric fields. Consequently, instead of the initial "simple" situation of an electromagnetic wave originating from OJlt source, we now have a complicated collective vibration of all the charges in the material. These induced fields add up onto the initial source fields. This complicated situation is described by a set of

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