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JEE Advanced 2016 Paper 1
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© examsnet.com
Question : 8
Total: 54
A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced.Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10cm away from the lens. Which of the following statement(s) is(are) true?
The refractive index of the lens 2.5.
The radius of curvature of the convex surface is 45 cm.
The faint image is erect and real.
The focal length of the lens is 20 cm.
Validate
Solution:
For lens
1
v
−
1
u
=
1
f
1
60
−
1
(
−
30
)
=
1
f
⇒
f
=
20
c
m
....(i)
Also
1
f
=
(
n
−
1
)
(
1
R
−
1
∞
)
=
(
n
−
1
)
R
.......(ii)
For reflection from convex mirror (curved surface)
1
v
+
1
u
=
1
f
=
2
R
1
+
10
+
1
−
30
=
1
f
=
2
R
......(iii)
R
=
30
cm
from (i),(ii) and (iii)
n
=
2.5
,
faint image erect & virtual
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