Question

two lenses one converging of focal length 30 cm make a combination of other lens and this combination behave Like a diverging lens of focal length 10 cm. find focal length of unknown lens and its nature also​

Answer 1

GiveN :

• Focal length of first converging lens $\sf{F_1\ =\ 30\ cm}$
• Focal length of combination of lenses $\sf{F_{eq}\ =\ - 10\ cm}$

To FinD :

• Focal length of Unknown lens

SolutioN :

As we know that for my last for focal length of lenses, if they are in combination is given by :

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$\implies \boxed{\sf{\dfrac{1}{F_{eq}} = \dfrac{1}{F_1} + \dfrac{1}{F_2}}}$

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Putting Values,

$\implies \rm{\dfrac{1}{-10} = \dfrac{1}{30} + \dfrac{1}{F_2}}$

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$\implies \rm{\dfrac{-1}{10} - \dfrac{1}{30} = \dfrac{1}{F_2}}$

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$\implies \rm{\dfrac{1}{F_2} = \dfrac{-3 - (+1)}{30}}$

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$\implies \rm{\dfrac{1}{F_2} = \dfrac{-3 - 1}{30}}$

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$\implies \rm{\dfrac{1}{F_2} = \dfrac{-4}{30}}$

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$\implies \rm{F_2 = \dfrac{-30}{4}}$

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$\implies \rm{F_2\ =\ -7.5\ cm }$

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• Nature of Lens is diverging (concave lens)
• Focal length is - 7.5 cm

Answer 2

GivEn:-

• Focal length of 1st converging lens $\sf ( f_1 )$ = 30cm

• Focal length of combination lenses = $\sf ( f_{eq} )$

To find:-

• Focal length of unknown lens and its nature also.

SoluTion:-

As we know that,

If we have combination of lenses then,

Sum of two lenses is equals to combination of these lenses.

Therefore,

$\dag\;{\underline{\boxed{\bf{\pink{ \dfrac{1}{ f_{eq} } = \dfrac{1}{ f_1 } + \dfrac{1}{ f_2 }}}}}}$

★ Now, Put value in above formula,

$:\implies\sf \dfrac{1}{-10} = \dfrac{1}{30} + \dfrac{1}{ f_2 }$

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$:\implies\sf - \dfrac{1}{10} - \dfrac{1}{30} = \dfrac{1}{ f_2 }$

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$:\implies\sf \dfrac{ - 3 - ( + 1)}{30}= \dfrac{1}{ f_2 }$

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$:\implies\sf \dfrac{ - 3 - 1}{30}= \dfrac{1}{ f_2 }$

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$:\implies\sf \dfrac{ - 4}{30}= \dfrac{1}{ f_2 }$

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$:\implies\sf f_2 = - \dfrac{30}{4}$

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$:\implies\sf{\underline{\boxed{\bf{\purple{ f_2 = -7.5\;cm}}}}}$ ★

Therefore, we can say that first lens of focal length 30cm and the other of focal length -7.5 combine to form a lens of focal length 10cm.

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We gets focal length of lens is -7.5cm.

Therefore, the nature of lens is diverging ( concave lens).

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