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Tardigrade
Question
Physics
A narrow parallel beam of light is incident on a transparent sphere of refractive index n . If the beam finally gets focussed at a point situated at a distance = 2 × (radius of sphere) from the centre of the sphere, then find n ?
Q. A narrow parallel beam of light is incident on a transparent sphere of refractive index
n
. If the beam finally gets focussed at a point situated at a distance
=
2
×
(radius of sphere) from the centre of the sphere, then find
n
?
836
184
NTA Abhyas
NTA Abhyas 2022
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A
3
4
B
2
3
C
−
6
4
D
3
−
2
Solution:
From first refraction
v
μ
2
−
u
μ
1
=
R
μ
2
−
μ
1
A
I
1
n
−
∞
1
=
R
n
−
1
A
I
′
=
n
−
1
n
R
for 2 nd refraction
u
=
B
I
′
=
A
I
′
−
2
R
=
n
−
1
n
R
−
2
R
=
n
−
1
(
n
−
2
n
+
2
)
R
u
=
(
n
−
1
)
(
2
−
n
)
R
apply
v
μ
2
−
u
μ
1
=
R
μ
2
−
μ
1
R
1
−
(
2
−
n
)
R
n
(
n
−
1
)
=
−
R
1
−
n
−
(
2
−
n
)
R
n
(
n
−
1
)
=
R
n
−
1
−
R
1
(
n
−
2
)
n
(
n
−
1
)
=
(
n
−
2
)
n
(
n
−
1
)
=
(
n
−
2
)
2
n
2
−
n
=
n
2
+
4
−
4
n
3
n
=
4
n
=
3
4