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Section:
Physics
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Question : 25 of 59
Marks:
+1
,
-0
A thin convex lens is made of two materials with refractive indices
n
1
n_1
n
1
and
n
2
n_2
n
2
, as shown in figure. The radius of curvature of the left and right spherical surface are equal. f is the focal length of the lens when
n
1
=
n
2
=
n
n_1=n_2=n
n
1
=
n
2
=
n
.The focal length is
f
+
Δ
f
f+\Delta f
f
+
Δ
f
when
n
1
=
n
n_1=n
n
1
=
n
and
n
2
=
n
+
Δ
n
n_2=n+\Delta n
n
2
=
n
+
Δ
n
.Assuming
Δ
n
≪
(
n
−
1
)
\Delta n \ll (n-1)
Δ
n
≪
(
n
−
1
)
and
1
≪
2
1 \ll 2
1
≪
2
,the correct statement(s) is/are,
[JEE Adv 2019 P1]
If
Δ
n
n
<
0
\frac{\Delta n}{n} < 0
n
Δ
n
<
0
then
Δ
f
f
>
0
\frac{\Delta f}{f} > 0
f
Δ
f
>
0
For
n
=
1.5
,
Δ
n
=
1
0
−
3
n = 1.5,\; \Delta n = 10^{-3}
n
=
1.5
,
Δ
n
=
1
0
−
3
and
f
=
20
c
m
f = 20\,\mathrm{cm}
f
=
20
cm
,the value of
∣
Δ
f
∣
|\Delta f|
∣Δ
f
∣
will be 0.02 cm (rounded off to 2nd decimal place).
The relation between
Δ
f
f
\;\; \frac{\Delta f}{f}
f
Δ
f
and
Δ
n
n
\;\; \frac{\Delta n}{n}
n
Δ
n
remains unchanged if both the convex surfaces arereplaced by concave surface of the same radius of curvature.
∣
Δ
f
f
∣
<
∣
Δ
n
n
∣
\left|\;\; \frac{\Delta f}{f}\right| < \left|\;\; \frac{\Delta n}{n}\right|
f
Δ
f
<
n
Δ
n
Validate
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