P1. Two layers of glass are placed on top of each other. The light is travelling
from n = 1.45 to n = 1.40. Find the range of angles , for which total internal reflection takes place.
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Critical angle is given by:
θ
c
=sin
−1
(1/μ)
For ray 1,
i=45
o
=sin
−1
(
1.414
1
)
θ
c1
=sin
−1
(
1.35
1
)>sin
−1
(
1.414
1
)
Hence, θ
c1
>i
Ray will not undergo total internal reflection.
Applying snell's law,
1.35sin(45)=1sin(θ
r
)
sin(θ
r
)=0.9545
θ
r
≈72
o
For ray 2,
i=45
o
=sin
−1
(
1.414
1
)
θ
c2
=sin
−1
(
1.45
1
)
θ
c2
=sin
−1
(
1.45
1
)<sin
−1
(
1.414
1
)
Hence, θ
c1
<i
Ray will undergo total internal reflection.
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