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Manipal Entrance Test 2015 Physics Paper
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© examsnet.com
Question : 17
Total: 50
A rectangular glass slab
A
B
C
D
of refractive index
n
1
is immersed in water of refractive index
n
2
(
n
1
>
n
2
)
.
A ray of light is incident at the surface
A
B
of the slab as shown. The maximum value of the angle of incidence
α
max
such that the ray comes out only from the another surface
C
D
is given by
sin
−
1
[
n
1
n
2
cos
(
sin
−
1
(
n
2
n
1
)
)
]
sin
−
1
[
n
1
cos
(
sin
−
1
(
1
2
)
)
]
sin
−
1
(
n
1
n
2
)
sin
−
1
(
n
2
n
1
)
Validate
Solution:
Rays comes out only from CD, means rays after refraction from AB get totally internally reflected at AD.
From the figure,
r
1
+
r
2
=
90
⇒
r
1
=
90
−
r
2
(
r
1
)
max
=
90
°
−
(
r
2
)
max
and
(
r
2
)
min
=
θ
C
(for total internal reflection at AD)
where,
sin
θ
C
=
n
2
n
1
or
θ
C
=
sin
−
1
(
n
2
n
1
)
∴
(
r
1
)
max
=
90
°
−
θ
C
Now, applymg Snell’s law at face AB, we wet
n
1
n
2
=
sin
α
max
sin
(
r
1
)
max
=
sin
α
max
sin
(
90
−
θ
C
)
=
sin
α
max
cos
θ
C
sin
α
max
=
n
1
n
2
cos
θ
C
∴
α
max
=
sin
−
1
[
n
1
n
2
cos
θ
C
]
=
sin
−
1
[
n
1
n
2
cos
(
sin
−
1
(
n
2
n
1
)
)
]
© examsnet.com
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