Question

Two lenses of power +3.5 D and -1.5 D are placed in contact . What is the power and the focal length of the combination ? If an object be placed at a distance of 0.8 m from the lens combination , where is the image formed ?

Answer 1

Power of combination of lensed

=P1+P2

=3.5-1.5

=2D

Power =1/focal length

2=1/focal length

Focal length=1/2

Focal length= 0.5metres

Hope it helps

Answer 2

The power of the combination is 2.0 D, the focal length of the lens is 0.5 m and the image is formed at 1.33 m.  

Explanation:

Given that,

Power of first lens = 3.5 D

Power of second lens = -1.5 D

We need to calculate the power of the combination

Using formula of power

$P=P_{1}+P_{2}$

Put the value into the formula

$P=3.5-1.5$

$P=2.0\ D$

We need to calculate the focal length

Using formula of power

$P = \dfrac{1}{f}$

$f=\dfrac{1}{P}$

Put the value in to the formula

$f=\dfrac{1}{2.0}$

$f=0.5\ m$

We need to calculate the image distance

Using formula of lens

$\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}$

Put the value into the formula

$\dfrac{1}{0.5}=\dfrac{1}{v}+\dfrac{1}{0.8}$

$\dfrac{1}{v}=\dfrac{1}{0.5}-\dfrac{1}{0.8}$

$\dfrac{1}{v}=\dfrac{3}{4}$

$v=1.33\ m$

Hence, The power of the combination is 2.0 D, the focal length of the lens is 0.5 m and the image is formed at 1.33 m.  

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Topic : power of lens

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