21. A plano convex lens fits exactly into a plano
concave lens. Their plane surfaces are parallel to
each other. If lenses are made of different materials
of refractive indices u, and u, and R is the radius
of curvature of the curved surface of the lenses, then
the focal length of the combination is [NEET-2013]
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pls refer the attachment
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1
Explanation:
Lens maker formula:
f
1
=(μ−1)(
R
1
1
−
R
2
1
) .......(1)
For Plano-convex lens: R
1
=∞ R
2
=−R
Using (1),
f
1
1
=(μ
1
−1)(
∞
1
−
−R
1
) ⟹
f
1
1
=
R
μ
1
−1
For Plano-concave lens: R
1
=−R R
2
=∞
Using (2),
f
2
1
=(μ
2
−1)(
−R
1
−
∞
1
) ⟹
f
2
1
=
R
1−μ
2
Thus focal length of combination,
F
1
=
f
1
1
+
f
2
1
=
R
μ
1
−1
+
R
1−μ
2
⟹ F=
μ
1
−μ
2
R
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