The refractive indices of water and glass are \(\frac43\)and \(\frac32

1.	The refractive indices of water and glass are \(\frac43\)and \(\frac32\)respectively. Write the relation and find the value of refractive index of water with respect to glass and glass with respect to water.
Answer» Refractive index of air, μair = 1; Given; Refractive index of water w.r.t air, ^aμ_w = \(\frac43\) Refractive index of glass w.r.t air, ^aμ_g = \(\frac32\) Refractive index of water w.r.t glass = ^gμ_w = \(\frac{^aμ_w}{^aμ_g{^c}}=\frac{\frac43}{\frac32}\) ⇒^gμ_w = \(\frac{4\times2}{3\times3}=\frac89\) ∴ Refractive index of water w.r.t glass is \(\frac89\) Also; Refractive index of water w.r.t glass. = \(\frac{1}{Refractive\,index\,of\,glass\,w.r.t\,water.}\) ⇒ Refractive index of glass w.r.t water = \(\frac{1}{Refractive\,index\,of\,water\,w.r.t\,glass}\) ∴ Refractive index of glass w.r.t water = \(\frac{1}{\frac89}=\frac98\) Refractive index of glass w.r.t water =\(\frac98\)

The refractive indices of water and glass are \(\frac43\)and \(\frac32\)respectively. Write the relation and find the value of refractive index of water with respect to glass and glass with respect to water.

Answer»

Refractive index of air, μair = 1;

Given;

Refractive index of water w.r.t air, ^aμ_w = \(\frac43\)

Refractive index of glass w.r.t air, ^aμ_g = \(\frac32\)

Refractive index of water w.r.t glass = ^gμ_w = \(\frac{^aμ_w}{^aμ_g{^c}}=\frac{\frac43}{\frac32}\)

⇒^gμ_w = \(\frac{4\times2}{3\times3}=\frac89\)

∴ Refractive index of water w.r.t glass is \(\frac89\)

Also;

Refractive index of water w.r.t glass. = \(\frac{1}{Refractive\,index\,of\,glass\,w.r.t\,water.}\)

⇒ Refractive index of glass w.r.t water = \(\frac{1}{Refractive\,index\,of\,water\,w.r.t\,glass}\)

∴ Refractive index of glass w.r.t water = \(\frac{1}{\frac89}=\frac98\)

Refractive index of glass w.r.t water =\(\frac98\)