Physics
Derive the condition for
sphemical abesuolion when two
lenses are separated by
a distance
Answers
Answer:
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Explanation:
Let two thin lenses are kept in contact.
For first lens we have
f
v
1
=(n
v
−1)(
R
1
1
−
R
2
1
)
and
f
R
1
=(n
R
−1)(
R
1
1
−
R
2
1
)
f
V
1
−
f
R
1
=(n
V
−n
R
)(
R
1
1
−
R
2
1
)
=
(n
Y
−1)
(n
V
−n
R
)
(n
Y
−1)(
R
1
1
−
R
2
1
)=
f
Y
ω
or
f
V
′
1
−
f
R
1
=
f
ω
(Letf
y
=f) ..... (1)
Similarly for second lens
f
V
′
1
−
f
R
′
1
=
f
′
ω
′
......... (2)
Adding equations (1) and (2)
(
f
V
1
+
f
V
′
1
)−(
f
R
1
+
f
R
′
1
)=
f
ω
+
f
′
ω
′
....... (3)
If the focal length of this lens combination for violet and red rays be F
V
and F
R
respectively then
f
V
1
+
f
V
′
1
=
F
V
1
and
f
R
1
+
f
R
′
1
=
F
R
1
So equation (3) becomes
F
V
1
−
F
R
1
=
f
ω
+
f
′
ω
′
But for achromatism of the lens combination, the focal length must be same for all colours of light so, F
V
=F
R
So,
f
ω
+
f
′
ω
′
=0
i.e.,
f
ω
+
f
′
ω
′
=0