Question

How is the refractive index of a medium related to the speed of light? Give an expression for refractive index of a medium with respect to another in terms of speed of light in these two media?

Answer 1

Explanation:

Refractive index compares the speed of light in a particular medium with the speed of light in vaccum.

It measures the optical density of a medium.

It should not be confused with the mass density of the medium.

For turpentile oil, it's mass density is less than water but optical density is more than that of water.

Now, moving on to your question, the relation between refractive index and speed of light:

refractive index (mu) = c (speed of light in vaccum) / v(speed of light in any medium)

for vaccum, refractive index = 1

This relation is also used in Snell's law..

Let the refractive index of medium 1 be u1...and the speed of light in medium1 be v1.

Therefore, u1 = c / v1 ----------equation1.

Similarly,

Let the refractive index of medium2 be u2 ...and the speed of light in medium 2 be v2..

Therefore, u2 = c / v2-----------equation2

Now,

⇒ u1 sin i = u2 sin r

⇒ sin i / sin r = u2 / u1     (Using equation 1 and 2....)

⇒ sin i / sin r = c / v2 × v1 / c

⇒ sin i / sin r = v1 / v2

Answer 2

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Tʜᴇ ʀᴇғʀᴀᴄᴛɪᴠᴇ ɪɴᴅᴇx ᴏғ ᴍᴇᴅɪᴜᴍ ᴡɪᴛʜ ʀᴇsᴘᴇᴄᴛ ᴛᴏ ᴍᴇᴅɪᴜᴍ ɪs ɢɪᴠᴇɴ ʙʏ ᴛʜᴇ ʀᴀᴛɪᴏ ᴏғ ᴛʜᴇ sᴘᴇᴇᴅ ᴏғ ʟɪɢʜᴛ ɪɴ ᴍᴇᴅɪᴜᴍ ᴛᴏ ᴛʜᴇ sᴘᴇᴇᴅ ᴏғ ʟɪɢʜᴛ ɪɴ ᴍᴇᴅɪᴜᴍ . Tʜɪs ɪs ᴜsᴜᴀʟʟʏ ʀᴇᴘʀᴇsᴇɴᴛᴇᴅ ʙʏ ᴛʜᴇ sʏᴍʙᴏʟ ɴ₂₁. Tʜɪs ᴄᴀɴ ʙᴇ ᴇxᴘʀᴇssᴇᴅ ɪɴ ᴀɴ ᴇǫᴜᴀᴛɪᴏɴ ғᴏʀᴍ ᴀs sʜᴏᴡɴ ʙᴇʟᴏᴡ.

${\boxed{\tt{\purple{n₂₁ = \frac{Speed \: of \: light \: in \: medium \: 1}{Speed \: of \: light \: in \: medium \: 2} = \frac{v₁}{v₂} }}}}$

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