Question

the speed of light in water is 2.2.5 x10^8m/s. if the speed of light in Vaccum be 3x10^8m/s, calculate the refractive index of water.
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Answer 1

Given:-

• Speed of light in water, v = 2.25 × 10^8  m/s
• Speed of light in vacuum, c = 3 × 10^8  m/s

To find:-

• Refractive index of water, n =?

Knowledge required:-

• The refractive index of a medium with respect to air or vacuum is known as Absolute refractive index of that medium.
• The absolute refractive index of a medium 'n' is given by the ratio of the speed of light in air/vacuum 'c' and speed of light in given medium 'v'.

        n = c / v

Solution:-

Here, we need to find the absolute refractive index of Water (n=?)

Using formula

→ n = c / v

[ putting values of c and v ]

→ n = ( 3 × 10^8 m/s ) / ( 2.25 × 10^8 m/s )

→ n = 3 / 2.25

→ n = 300 / 225

→ n = 4 / 3  

Therefore,

• Refractive index (absolute) of water is 4/3.

Answer 2

Answer:

Correct Question :-

• The speed of light in water is 2.25 × 10⁸ m/s. If the speed of light in vaccum be 3 × 10⁸ m/s. Calculate the refractive index of water.

Given :-

• The speed of light in water is 2.25 × 10⁸ m/s.
• The speed of light in vaccum is 3 × 10⁸ m/s.

To Find :-

• What is the refractive index of water.

Formula Used :-

$\boxed{\bold{\large{n\: =\: \dfrac{c}{v}}}}$

where,

• n = Index of refraction
• c = Speed of light in vaccum
• v = Speed of light in water

Solution :-

$\sf Given \begin{cases} & \sf{Speed\: of\: light\: in\: vaccum = \bf{3\; \times {10}^{8}\: m/s}} \\ & \sf{Speed\: of\: light\: in\: water = \bf{2.25\; \times {10}^{8}\: m/s}} \end{cases}$

According to the question by using the formula we get,

⇒ n = $\dfrac{3 \times {10}^{8}}{2.25 \times {10}^{8}}$

⇒ n = $\sf\dfrac{3 \times 100000000}{2.25 \times 100000000}$

⇒ n = $\dfrac{3}{2.25}$

⇒ n = $\dfrac{3 \times 100}{225}$

⇒ n = $\dfrac{300}{225}$

⇒ n = $\sf\dfrac{\cancel{300}}{\cancel{225}}$

⇒ n = $\dfrac{4}{3}$

➠ n = 1.33

$\therefore$ The refractive index of water is 1.33 .