Question

If the speed of light in water is 2.25x108m/s and the speed in vacuum is 3x10 m/s.
Calculate the refractive index of water?​

Answer 1

$\huge{\tt{\underline{Given:-}}}$

• Speed of light in water :- 2.25×10^8 m/s

• Speed of light in vacuum:- 3×10^8 m/s

$</p><p>\huge{\tt{\underline{To\:Find:-}}}}$

• Refractive index (n):-???

$</p><p>\huge{\tt{\underline{Solution:-}}}}$

As we know, refractive index of medium 2 with respect to medium 1 is:-

${ \tt{n = \frac{speed \: of \: light \: in \: medium \: 1}{speed \: of \: light \: in \: medium \: 2} }}$

Here the medium 1 is vacuum so absolute refractive index would be

${ \boxed{{ \tt{n = \frac{c}{v} }}}}$

Putting the values;

${ \tt{n = \frac{3 \times 10 {}^{ 8} }{2.25 \times 10 {}^{8} } }} \\ { \tt{n = \frac{3 \times{ \cancel{ 10 {}^{8}}} }{2.25 \times { \cancel{10 {}^{8} }}}} } \\ { \boxed{ \bf{ n = 1.33 }}}$

•°• The refractive index is 1.33

$\huge{\tt{\underline{Concept:-}}}$

★The refractive index or index of refraction of a material is a dimensionless number that describes how fast light travels through the material. It is defined as. where c is the speed of light in vacuum and v is the phase velocity of light in the medium.

__________________________________

Answer 2

Correct Question:

If the speed of light in water is 2.25x10⁸ m/s and the speed in vacuum is 3x10⁸ m/s. Calculate the refractive index of water?

Answer:

• Refraction Index (μ) of Water is 1.33.

Given:

1. Speed of Light in Water (v₂) = 2.25 × 10⁸ m/s.
2. Speed of Light in Vaccum (v₁) = 3 × 10⁸ m/s.

Explanation:

$\rule{300}{1.5}$

From the Formula we Know,

$\large \bigstar \: {\boxed{\tt n_{water} = \dfrac{v_1}{v_2}}}$

$\bold{Here}\begin{cases}\tt{n} \text{ Denotes Refractive index of Water} \\ \tt{v_1} \text{ Denotes Speed of Light in Vaccum} \\ \tt{v_2} \text{ Denotes Speed of Light in Water}\end{cases}$

Now,

$\large{\boxed{\tt n_{water} = \dfrac{v_1}{v_2}}}$

Substituting the values,

$\large{\tt \hookrightarrow n_{water} = \dfrac{3 \times 10^8 \: m/s}{2.25 \times 10^8 \: m/s}}$

$\large{\tt \hookrightarrow n_{water} = \dfrac{3 \times 10^8}{2.25 \times 10^8}}$

$\large{\tt \hookrightarrow n_{water} = \dfrac{3}{2.25} \times \dfrac{10^8}{10^8}}$

$\large{\tt \hookrightarrow n_{water} = \dfrac{3}{2.25} \times \cancel{\dfrac{10^8}{10^8}}}$

$\large{\tt \hookrightarrow n_{water} = \cancel{\dfrac{3}{2.25}} \times 1}$

$\large{\tt \hookrightarrow n_{water} =1.33 \times 1}$

$\large\hookrightarrow{\underline{\boxed{\red{\tt n_{water} =1.33}}}}$

∴ Refraction Index (μ) of Water is 1.33.

$\rule{300}{1.5}$

$\rule{300}{1.5}$

$\large\boxed{\begin{minipage}{7 cm} \bigstar \: {\underline{\underline{\tt Important \: Formulas}}}: \\\\ \star \; \tt \dfrac{\sin i}{\sin r} = Refractive \: Index(n) \\\\\\ \star \; \tt Lens \: Formula \rightarrow \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} \\\\\\ \star \: \tt Mirror \: Formula \rightarrow \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}\\\\\\ \underline{Note:} \\\\ \star \: \text{f Denotes Focal Length} \\\\ \star \: \text{v Denotes Image Distance} \\\\ \star \: \text{u Denotes Object Distance} \end{minipage}}$

$\rule{300}{1.5}$