Question

speed of light in water is 2.25x10^8 m/s and in glass is 2x 10^8 m/s (a) Find refracture index in each case . (b)Which of the two is optically denser. ​

Answer 1

Solution :

✴ Given :-

▪ Velocity of light in water = 2.25 × 10$^8$mps

▪ Velocity of light in glass =2 × 10$^8$mps

✴ To Find :-

▪ Refractive index of water and glass

▪ Which of the two medium is optically denser

✴ Concept :-

✏ Refractive index of medium is defined as ratio of velocity of light in vacuum to the velocity of light in medium.

✴ Calculation :-

$\implies\bf\:\mu_{water}=\dfrac{velocity\:of\:light\:in\:vacuum}{velocity\:of\:light\:in\:water}\\ \\ \implies\sf\:\mu_{water}=\dfrac{3\times 10^8}{2.25\times 10^8}\\ \\ \implies\:\boxed{\bf{\pink{\mu_{water}=\dfrac{4}{3}=1.33}}}$

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$\leadsto\bf\:\mu_{glass}=\dfrac{velocity\:of\:light\:in\:vacuum}{velocity\:of\:light\:in\:glass}\\ \\ \leadsto\sf\:\mu_{glass}=\dfrac{3\times 10^8}{2\times 10^8}\\ \\ \leadsto\:\boxed{\purple{\bf{\mu_{glass}=\dfrac{3}{2}=1.5}}}$

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$\dashrightarrow\sf\:\mu_{glass}>\mu_{water}\\ \\ \therefore\bf{\blue{glass\:is\:optically\:more\:denser\:than\:water.}}$

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✴ Additional information :-

• Refractive index is an unitless as well as dimensionless quantity.

Answer 2

Answer:

Given:

Speed of light in water = 2.25 × 10^8 m/s

Speed of light in glass = 2 × 10^8 m/s

To find:

• Refractive Index in each media
• Which media is optically denser ?

Concept:

Refractive Index is a dimension-less Quantity represented by the ratio of velocity of light in vacuum to the velocity of light in a particular medium.

Calculation:

We know that velocity of light in vacuum is 3 × 10^8 m/s

Refractive Index of glass :

$\mu_{glass} = \dfrac{3 \times {10}^{8} }{2 \times {10}^{8} } = 1.5$

Refractive Index of Water :

$\mu_{water} = \dfrac{3 \times {10}^{8} }{2.25 \times {10}^{8} } = 1.33$

Refractive Index is directly proportional optical density :

So Glass is more optically denser than Water