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JEE Advanced 2023 Paper 1 Solutions
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© examsnet.com
Question : 9
Total: 51
An optical arrangement consists of two concave mirrors
M
1
and
M
2
, and a convex lens
L
with a common principal axis, as shown in the figure. The focal length of
L
is
10
cm
. The radii of curvature of
M
1
and
M
2
are
20
cm
and
24
cm
, respectively. The distance between
L
and
M
2
is
20
cm
. A point object
S
is placed at the mid-point between
L
and
M
2
on the axis. When the distance between
L
and
M
1
is
n
7
cm
, one of the images coincides with
S
. The value of
n
is__________
80
150
200
220
Validate
Solution:
For reflection from
M
2
1
v
+
1
(
−
10
)
=
1
(
−
12
)
1
v
=
1
10
−
1
12
v
=
+
60
cm
(
for
I
1
)
For refraction from
L
1
v
−
1
u
=
1
f
1
v
−
1
(
−
80
)
=
1
10
v
=
+
80
7
(
For
I
2
)
This image should be at focus of
M
1
∴
20
2
+
80
7
=
n
7
n
=
150
Also,
If
I
2
is formed at pole of
M
1
then
n
∕
7
=
80
∕
7
n
=
80
And further if
I
2
is formed at centre of curvature of
M
1
then
n
7
=
80
7
+
20
∴
n
=
220
© examsnet.com
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