Question

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.

Answer 1

We know

$\boxed{\sf n_{21}=\dfrac{C}{V}}$

How he find:-

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

$\\ \sf\longmapsto n_D=\dfrac{C}{V_D}$

$\\ \sf\longmapsto 2.4=\dfrac{3\times 10^8ms^{-1}}{V_D}$

$\\ \sf\longmapsto V_D=\dfrac{3\times 10^8ms^{-1}}{2.4}$

$\\ \sf\longmapsto V_D=1.25\times 10^8ms^{-1}$

$\\ \sf\longmapsto V_D=125\times 10^6ms^{-1}$

For rutile

$\\ \sf\longmapsto n_R=\dfrac{C}{V_R}$

$\\ \sf\longmapsto V_R=\dfrac{C}{n_R}$

$\\ \sf\longmapsto V_R=\dfrac{3\times 10^8ms^{-1}}{2.9}$

$\\ \sf\longmapsto V_R=1.03\times 10^8$

$\\ \sf\longmapsto V_R=103\times 10^6ms^{-1}$