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JEE Advanced 2020 Full Test 5 Paper 1
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© examsnet.com
Question : 5
Total: 54
A planoconvex lens
(
µ
=
1.5
)
of focal length
20
c
m
has its plane side silvered. Which of the following statements is\/are correct?
The radius of curvature of its curved surface is half that of a surface of equiconvex lens of focal length
20
c
m
made of same material
An object placed at
15
c
m
on the axis on the convex side gives rise to an image at a distance of
30
c
m
from it
An object placed at a distance of
20
c
m
on the axis on the convex side gives rise to an image at
40
c
m
from it
It acts as a convex mirror
Validate
Solution:
1
F
=
(
µ
−
1
)
R
=
1
20
⇒
20
=
R
(
µ
−
1
)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
(
1
)
If equiconvex lens of
f
=
20
Then
1
20
=
(
µ
−
1
)
2
R
From equation (1) and (2) we conclude
∴
R
=
40
(
µ
−
1
)
That option (A) is correct.
−
1
f
L
=
(
µ
−
1
)
[
1
R
−
1
∞
]
=
(
µ
−
1
)
R
for refraction at the convex surface
∴
power
P
L
=
1
f
L
=
−
(
µ
−
1
)
R
For reflection at the silvered plane surface
F
M
=
α
∴
power
P
M
=
0
For refraction at the convex surface again
P
L
=
(
µ
−
1
)
R
Hence power of the system
P
=
P
L
+
P
M
+
P
L
=
2
P
L
+
P
M
=
−
2
(
µ
−
1
)
R
∴
focal length of the system
F
=
1
P
=
−
R
2
(
µ
−
1
)
=
−
10
c
m
u
=
−
15
c
m
© examsnet.com
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