Question

Find the speed of light in glass if the refractive index of glass is 1.5 and c=3×10^8 m/s​

Answer 1

GIVEN :-

• Speed of light in vaccum/air ( c ) = 3 × 10⁸ m/s.
• Refractive index of glass ( μg ) = 1.5 .

TO FIND :-

• The speed of light in glass ( Vg)

SOLUTION :-

As we know that,

$: \implies \: \displaystyle \sf \: \mu_{g} = \frac{c}{v_g}$

$: \implies \: \displaystyle \sf \: 1.5 = \frac{3 \times 10 ^{8} }{v_g }$

$: \implies \: \displaystyle \sf \: {v_g } \times 1.5 = 3 \times 10 ^{8}$

$: \implies \: \displaystyle \sf \: {v_g } = \frac{3 \times 1 0 ^{8} }{1.5}$

$: \implies \underline{ \boxed{ \displaystyle \sf \: {v_g } = 2 \times 10 ^{8} \: ms ^{ - 1} }}$

Hence the speed of the light in glass is 2 × 10⁸ m/s.

Answer 2

Given:-

❏Refractive Index = 1.5

❏Speed of light in vaccum = 3×10⁸ m/s

Find:-

❏Speed of light in glass

Solution:-

we, know that

$\huge{\underline{\boxed{\sf \mu = \dfrac{c}{v} }}}$

where,

• Refractive Index, $\mu$ = 1.5
• Speed of light in vaccum, c = 3×10⁸ m/s

So,

⇨ $\green{\sf \mu = \dfrac{c}{v}}$

⇨ $\green{\sf v = \dfrac{c}{\mu}}$

⇨ $\green{\sf v = \dfrac{3×10^8}{1.5}}$

⇨ $\green{\sf v = \dfrac{3×10^9}{15}}$

⇨ $\green{\sf v = \dfrac{10^9}{5}}$

⇨ $\green{\sf v = \dfrac{1000000000}{5}}$

⇨ $\green{\sf v = 200000000 m/s}$

⇨ $\green{\sf v = 2\times 10^8 m/s}$

$\small{\therefore\sf v = 2\times 10^8 m/s}$

Hence, Speed of light in the vaccum is 2×10⁸m/s