A jewellery shop owner has two identical clear gemstones but cannot remember which one is diamond and which one is rutile. Rutile is a clear gemstone that appears identical to a diamond. It is often used as a cheaper alternative to diamond in jewellery. She is aware that the refractive index of diamond is 2.4 and the refractive index of rutile is 2.9. She has a machine capable of measuring the speed of light through each material and basic measuring equipment. Briefly describe how the shop owner can distinguish between the diamond and rutile gemstones. Use calculations to support your answer.

The owner will measure speed of light through the index(Diamond or rutile).Then using calculations he fill find which is the velocity of diamond or rutile

For diamond

[tex]\\ \sf\longmapsto n_D=\dfrac{C}{V_D}[/tex]

[tex]\\ \sf\longmapsto 2.4=\dfrac{3\times 10^8ms^{-1}}{V_D}[/tex]

[tex]\\ \sf\longmapsto V_D=\dfrac{3\times 10^8ms^{-1}}{2.4}[/tex]

[tex]\\ \sf\longmapsto V_D=1.25\times 10^8ms^{-1}[/tex]

[tex]\\ \sf\longmapsto V_D=125\times 10^6ms^{-1}[/tex]

For rutile

[tex]\\ \sf\longmapsto n_R=\dfrac{C}{V_R}[/tex]

[tex]\\ \sf\longmapsto V_R=\dfrac{C}{n_R}[/tex]

[tex]\\ \sf\longmapsto V_R=\dfrac{3\times 10^8ms^{-1}}{2.9}[/tex]

[tex]\\ \sf\longmapsto V_R=1.03\times 10^8[/tex]

[tex]\\ \sf\longmapsto V_R=103\times 10^6ms^{-1}[/tex]

facundo3141592 facundo3141592 · Answer 2 · 2021-08-31T18:46:00+02:00

When an electromagnetic wave (like light) travels in a given medium, the speed of the wave in the medium depends on the refractive index of the material.

Such that if the refractive index is n₀, the speed of the wave in that material will be:

v = c/n₀

where c is the speed of light in vacuum.

c = 3×10^8 m/s

Now, we know that:

the refractive index of diamond is 2.4

the refractive index of rutile is 2.9

And the owner can measure (in some way) the speed of light through each material.

Looking at the equation of the speed of the wave in a material, we can see that as the index of refraction increases, the velocity should decrease.

Then when the light travels in the rutile (which has a larger index) it will have a smaller velocity than in diamond.

Where the speed in rutile is:

[tex]V_r = \frac{3\cdot 10^8 m/s}{2.9} = 103,448,275.1 m/s[/tex]

And in diamond is:

[tex]V_r = \frac{3\cdot 10^8 m/s}{2.4} = 125,000,000 m/s[/tex]

So measuring the speeds in each cristal, she can know which one is diamond and which one is rutile.

If you want to learn more, you can read:

https://brainly.com/question/2660868