Question

the refractive index of water is 4/3 and speed of light in air is 3×10^8.find speed of light in the water.​

Answer 1

GivEn:

• refractive index of water is $\sf \dfrac{4}{3}$

• Speed of light in air is 3 × $\sf 10^8$

To find:

• Speed of light in the water.

SoluTion:

Refractive Index is the measure of bending of light when it passes from one medium to another medium.

It is the ratio of speed of light (c) in empty space or a vaccum to speed of light (v) in medium.

$:\implies\sf \purple{Refractive\;index = \dfrac{Speed\;of\;light\;in\;air}{Speed\;of\;light\;in\;medium}}\\\\ :\implies\sf n = \dfrac{c}{v}\\\\ {\underline{\bf{\bigstar\;Now,\; According\;to\; Question\;:}}}\\\\ \;\;\;\bullet\;\;\sf refractive\; index\; of \;water \;is\; \dfrac{4}{3}\\\\ \;\;\;\bullet\;\;\sf Speed\; of \;light\; in \;air \;is\; 3 \times 10^8$

Here,

★ Given Medium (v) is water.

$\maltese\;{\boxed{\sf{\pink{Refractive\;index = \dfrac{Speed\;of\;light\;in\;air}{Speed\;of\;light\;in\;water}}}}}\\\\ \dashrightarrow\sf \dfrac{4}{3} = \dfrac{3 \times 10^8}{v}\\\\ \dashrightarrow\sf v = 3 \times 10^8 \times \dfrac{3}{4}\\\\ \dashrightarrow{\underline{\boxed{\sf{\purple{v = 2.25 \times 10^8\;m/s}}}}}\;\bigstar\\\\ \therefore\;\sf \underline{Speed\;of\;light\;in\;water\;is\; \bf{2.25 \times 10^8\;m/s}}.$