Two light rays, one incident at an angle theta 1 = 60 degree onto a glass plate

Question

Two light rays, one incident at an angle theta 1 = 60 degree onto a glass plate (Fig 2a), and another incident normally on an identical glass plate (Fig 2b). Both plates are in air. The index of refraction for the glass plates is n = 1.5, and the thickness of each plate is h = 2.2 m In the figure below determine whether or not the ray will emerge from the other side. Support your answer with relevant calculations. In case light in (a) emerges from the other side, determine the angle with which the ray will emerge into air. What would be the optical length that corresponds to the thickness of the plate traversed by the light ray in (b).

Explanation / Answer

a) Light emerges in both the cases

Proof::

sin(i)/sin(r)=n

==> sin(r)=sin(i)/1.5=sin(60 degrees)/1.5

==> r=35.26

now the angle of incidence is 35.26 degrees

==> sin(i2)/sin(r2)=1/n

==> sin(r2)=sin(35 degrees)*1.5

==> r2=60 degrees

so it emerges

b) angle of emergence=angle of incidence= 60 degrees with normal

c) optical path length = n*h=1.5*2.2=3.3 m

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