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Standard XII

Physics

Cutting of Thin Lenses

Two convex le...

Question

Two convex lenses of focal lengths $f_{1}$ and $f_{2}$ are arranged co-axially in a metal tube. What should be the distance between the lenses so that incident beam is parallel and emergent beam is also parallel?

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Solution

Consider lens 1:
Since the incident ray is parallel so $u = \infty$
So using lens equation
$\frac{1}{f_{1}} = \frac{1}{v} - \frac{1}{u}$
$v = f_{1}$
Now this image will act object for other lens.
Let the distance two lens be $d$ .
$u_{2} = - (d - f_{1})$
$v_{2} = \infty$
So $\frac{1}{f_{2}} = \frac{1}{v_{2}} - \frac{1}{u_{2}} = \frac{1}{d - f_{1}}$
$d = f_{1} + f_{2}$

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Two convex lenses of focal lengths f1 and f2 are arranged co-axially in a metal tube. What should be the distance between the lenses so that incident beam is parallel and emergent beam is also parallel?

Consider lens 1:Since the incident ray is parallel so u=∞So using lens equation1f1=1v−1uv=f1Now this image will act object for other lens.Let the distance two lens be d.u2=−(d−f1) v2=∞ So1f2=1v2−1u2=1d−f1d=f1+f2

Two convex lenses of focal lengths $f_{1}$ and $f_{2}$ are arranged co-axially in a metal tube. What should be the distance between the lenses so that incident beam is parallel and emergent beam is also parallel?