Question

two thin lenses have a combined power of+9D when they are separated by a distance of 20cm their equivalent power becomes+27/5Dtheir individual power in dioptre are​

Answer 1

Answer:

3,6

................

Answer 2

The individual power is 3 D and 6 D.

Explanation:

Given that,

Power of combination P= +9D

Distance = 20 cm

Equivalent power $P'= \dfrac{+27}{5}$

Let the power of each lens be P₁ and P₂

Power of combination of lenses is

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

$9=P_{1}+P_{2}$....(I)

We need to find the value of P₁P₂

Using formula of power

$P_{eq}'=P_{1}+P_{2}-d\times P_{1}P_{2}$

Put the value into the formula

$\dfrac{27}{5}=9-0.2(P_{1}P_{2})$

$P_{1}P_{2}=18$

$P_{2}=\dfrac{18}{P_{1}}$

Put the value of P₂ in the equation (I)

$9=P_{1}+\dfrac{18}{P_{1}}$

$P_{1}^2-9P_{1}+18=0$

$P_{1}=3\ D$

Then $P_{2} = 6\ D$

If $P_{1}=6\ D$

Then $P_{2} =3\ D$

Hence, The individual power is 3 D and 6 D.

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Topic : power of lens

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