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Two lenses of power 15D and -5D and in contact with each other forming a combination lense. What is the focal length of the combination lense? If an object is size 3cm is placed 30cm from this combination lenses. Calculate the position and size the image formed.

Two lenses of power 15D and -5D and in contact with each other forming a combination lense. What is the focal length of the combination lense? If an object is size 3cm is placed 30cm from this combination lenses. Calculate the position and size the image formed.

Grade:10

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
Dear student,

The individual powers of a combination of lenses can be added to obtain that of the combination.

HenceP'=P_1+P_2=15D-5D=10D

Hence the focal length of the combinationf'=\dfrac{1}{P'}=10cm

For the object,u=-30cm

Hence\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f'}
\implies \dfrac{1}{v}=\dfrac{1}{10}-\dfrac{1}{30}=\dfrac{1}{15} \implies v=15cm

Magnification=\dfrac{v}{u}=\dfrac{15}{-30}=-\dfrac{1}{2}

Hence an inverted image of size1.5cmis formed at a distance of15cmfrom the lens.

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