Question

The speed of light in glass is 2x108 m/s. What will be the speed of light in water if the
refractive index of glass with respect to water is 9/8 ?​

Answer 1

Given :

• Speed of light in glass, $\sf{v_g}$ = 2 × 10⁸ ms⁻¹

• Refractive index of glass with respect to water, $\sf{n_{gw}}$ = $\sf{\dfrac{9}{8}}$

To find :

• Speed of light in water, $\sf{v_w}$ = ?

Knowledge required :

• Refractive index (n) of medium A with respect to medium B is given by

$\bigstar\boxed{\sf{n_{AB}=\dfrac{speed\:of\:light\:in\:medium\:B}{speed\:of\:light\:in\:medium\:A}}}$

Solution :

using formula

$\implies\sf{n_{gw}=\dfrac{v_w}{v_g}}$

$\implies\sf{\dfrac{9}{8}=\dfrac{v_w}{2\times 10^8 \;\;ms^{-1}}}$

$\implies\sf{v_w=\dfrac{9}{4}\times 2 \times 10^8\;\;ms^{-1}}$

$\implies\sf{v_w=\dfrac{9}{4}\times 10^8\;\;ms^{-1}}$

$\implies\boxed{\boxed{\sf{v_w=2.25\times 10^8\;\;ms^{-1}}}}\;\;\;\purple{\bigstar}$

therefore,

• Speed of light in water would be 2.25 × 10⁸ ms⁻¹.

Answer 2

$\mathtt{\huge{\underline{\red{Question\:?}}}}$

★ The speed of light in glass is 2x10⁸m/s. What will be the speed of light in water if the refractive index of glass with respect to water is 9/8 ?

$\mathtt{\huge{\underline{\green{Answer:-}}}}$

✒The speed of light in water 2.25 × 10⁸ ms⁻¹.

$\mathtt{\huge{\underline{\pink{Concept\:Used:-}}}}$

• The refractive index of a medium for a light of given wavelength may be defined as the ratio of the speed of light in vacuum to its speed in that medium.

Refractive index = $\frac{Speed\:of\:Light(Medium 1)}{Speed\:of\:Light(Medium2)}$

Formulae :-

ngw = $\dfrac{<strong>v</strong>g}{<strong>w</strong>g}$

Factors on which the refractive index of a medium depends :-

1. Nature of the medium.

2. Wavelength of the light used.

3. Temperature.

4. Nature of the surrounding medium.

$\mathtt{\huge{\underline{\green{Solution:-}}}}$

Given :-

• The speed of light in glass is 2x108 m/s.

• The refractive index of glass with respect to water is 9/8.

To Find :-

• The speed of light in water.

Calculation :-

According to the question,

ngw = $\dfrac{vg}{wg}$

The refractive index of glass with respect to water .

Here, glass is rarer medium & water is denser.

ʀᴀʀᴇʀ ᴍᴇᴅɪᴜᴍ ➝ ᴅᴇɴsᴇʀ ᴍᴇᴅɪᴜᴍ

➝ $\sf{\dfrac{9}{8}=\dfrac{v_w}{2\times 10^8 \;\;ms^{-1}}}$

➝ $\sf{v_w=\dfrac{9}{4}\times 2 \times 10^8\;\;ms^{-1}}$

➝ $\sf{v_w=\dfrac{9}{4}\times 10^8\;\;ms^{-1}}$

➝ $\underline{\underline{\sf{v_w=2.25\times 10^8\;\;ms^{-1}}}}$

➡ So, The Speed of light in water would be 2.25 × 10⁸ ms⁻¹.