Question

A converging bundle of light rays in the shape of a cone with a vertex angle of 45°falls on a circular diaphragm of 20 cm diameter.A lens with power 5D is fixed in the diaphragm.Diameter of the face of lens is equal to that of diaphragm.If the vertex angle of new cone is theta,then tan theta=

Answer 1

Given that,

A converging bundle of light rays in the shape of a cone with a vertex angle of 45°

Diameter of circular diaphragm is 20 cm

Power of a lens is 5D

To find,

The vertex angle of new cone.

Solution,

Power of a lens,

$P=\dfrac{1}{f}$, f is focal length

$f=\dfrac{1}{P}\\\\f=\dfrac{1}{5}\\\\f=20\ cm$

Finding v or image distance using lens formula as :

$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}\\\\\dfrac{1}{v}=\dfrac{1}{u}+\dfrac{1}{f}\\\\\dfrac{1}{v}=\dfrac{1}{10}+\dfrac{1}{20}\\\\v=\dfrac{20}{3}\ cm$

Now using trigonometry,

$\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{10}{v}$, P is radius of face of lens and B is v i.e. image distance

So,

$\tan\theta=\dfrac{10}{\dfrac{20}{3}}\\\\\tan\theta=1.5$

Hence, the value of $\tan\theta$ is 1.5

Answer 2

Answer:

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Explanation:

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