Two convex lenses, each of focal length $$40$$ cm, are filled at the ends of a tube and the tube is filled with water μ$$=43$$. A beam of parallel rays parallel to the axis of the tube, enters the tube through one end and emerges from the tube as a beam of parallel rays of same diameter as the incident beam. If refractive index of glass is $$1.5$$, find the length l of the tube.

Question

Two convex lenses, each of focal length $$40$$ cm, are filled at the ends of a tube and the tube is filled with water μ$$=43$$. A beam of parallel rays parallel to the axis of the tube, enters the tube through one end and emerges from the tube as a beam of parallel rays of same diameter as the incident beam. If refractive index of glass is $$1.5$$, find the length l of the tube.

Infinity Learn · Accepted Answer

For each lens, if R be the radius of curvature of each convex surface, then $$1f=2$$μg−$$1R$$⇒$$R=21.5$$−$$1$$×$$40$$ cm⇒$$R=40$$ cmIf x and y be the second focal length and first focal lengths of lenses $$1$$ and $$2$$ respectively, then x $$=$$ y.For lens $$-$$ $$1$$, μ$$+x$$−$$1$$α$$=$$μg−$$1+R$$−μg−μ−R⇒μ$$x=2$$μg−μ−$$1R$$⇒$$4/3x=2$$×$$1.5$$−$$43$$−$$140$$⇒$$x=80$$ cm∴ $$l=x+y=x+x=80+80cm=160$$ cm

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