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KVPY SA Exam 2016 Question Paper
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© examsnet.com
Question : 67
Total: 80
A rectangular block is composed of three different glass prisms (with refractive indices
µ
1
,
µ
2
and
µ
3
) as shown in the figure below. A ray of light incident normal to the left face emerges normal to the right face. Then the refractive indices are related by
µ
1
2
+
µ
2
2
=
2
µ
3
2
µ
1
2
+
µ
2
2
=
µ
3
2
µ
1
2
+
µ
3
2
=
2
µ
2
2
µ
2
2
+
µ
3
2
=
2
µ
1
2
Validate
Solution:
for surface AB:
µ
1
sin
45
º
=
µ
2
sin
θ
1
… (1)
for surface AC:
µ
2
sin
(
ω
−
θ
1
)
=
µ
3
sin
45
µ
3
sin
45
º
=
µ
2
cos
θ
1
… (2) (ω = 90º)
Squaring and adding equation (1) & (2)
µ
1
2
2
+
µ
3
2
2
=
µ
2
2
⇒
µ
1
2
+
µ
3
2
=
2
µ
2
2
© examsnet.com
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