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Test Index
JEE Main Physics Class 12 Ray Optics and Optical Instruments Part 1 Questions
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© examsnet.com
Question : 84
Total: 99
A transparent solid cylindrical rod has a refractive index of
2
√
3
.
It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure.
The incident angle
θ
for which the light ray grazes along the wall of the rod is:
[2009]
sin
−
1
(
√
3
∕
2
)
sin
−
1
(
2
√
3
)
sin
−
1
(
1
√
3
)
sin
−
1
(
1
∕
2
)
Validate
Solution:
Applying Snell's law for medium inside the cylinder and air at
Q
we get
n
=
sin
90
°
sin
(
90
°
−
α
)
=
1
cos
α
∴
cos
α
=
1
n
∴
sin
α
=
√
1
−
cos
2
α
=
√
1
−
1
n
2
=
√
n
2
−
1
n
......(i)
Applying Snell’s Law for air and medium inside the cylinder at P we get
n
=
sin
θ
sin
α
⇒
sin
θ
=
n
×
sin
α
=
√
n
2
−
1
;
[from (i)]
∴
sin
θ
=
√
(
2
√
3
)
2
−
1
=
√
4
3
−
1
=
1
√
3
or
θ
=
sin
−
1
(
1
√
3
)
© examsnet.com
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