Question

.) A converging lens of refra
it is completely immersed in
dive index 1.5 has a power of 10 D. When
in a liquid, it behaves as a diverging lens
of focal length 50 cm. Find
the refractive index of the liquid.​

Answer 1

Answer:

Explanation:

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Answer 2

The refractive index of the liquid is 1.67.

Explanation:

Given that,

Refractive Index = 1.5

Power = 10 D

We need to calculate the focal length in glass

Using formula of power

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

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

Put the value into the formula

$f=\dfrac{100}{10}$

$f=10\ cm$

We need to calculate the refractive index of the liquid

Using formula of focal length

For glass,

$\dfrac{1}{f}=(\mu_{g}-1)(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}})$

Put the value into the formula

$\dfrac{1}{10}=(1.5-1)(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}})$...(I)

For water,

$\dfrac{1}{f}=(\dfrac{\mu_{g}}{\mu_{l}}-1)(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}})$

Put the value into the formula

$\dfrac{1}{-50}=(\dfrac{1.5}{\mu_{l}}-1)(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}})$....(II)

Divided equation (I) by equation (II)

$\dfrac{-50}{10}=\dfrac{1.5-1}{\dfrac{1.5}{\mu_{l}}-1}$

$\dfrac{1.5}{\mu_{l}}=\dfrac{1.5-1}{-5}$

$\mu_{l}=\dfrac{1.5}{0.9}$

$\mu_{l}=\dfrac{5}{3}$

$\mu_{l} = 1.67$

Hence, The refractive index of the liquid is 1.67.

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Topic : refractive index

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