Question

The refractive index of water is 4/3 and of glass is 3/2. What is the refractive index of glass with respect to water ?
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Answer 1

Information provided with us:

• Refractive index of water is 4/3
• Refractive index of glass is 3/2

What we have to calculate:

• Refractive index of glass with respect to water.

We know that,

• Refractive index of glass = $\sf{ _{a} \mu _{g}}$
• Refractive index of water =$\sf{ _{a} \mu _{w}}$

Refractive Index:

• It is typically a ratio of sine of angle of incidence in the first medium to the sine of the angle in second medium.

Refractive index of glass with respect to water is calculated by,

• $\red \bigstar \: \underline{ \boxed{\large{ \sf{ _{w}\mu{}_{g} = \dfrac{refractive \: index \: of \: water }{refractive \: index \: of \: water} }}}}$

Here we have,

• $\sf{ _{a} \mu _{w}} = {\dfrac{4}{3} }$

• $\sf{ _{a} \mu _{g}} = {\dfrac{3}{2} }$

Substituting the values,

$: \longmapsto \: \sf{ _{w} \mu _{g} \: = \: \dfrac{ \dfrac{3}{2} }{ \dfrac{4}{3} } }$

Now,

$: \longmapsto \: \sf{ _{w} \mu _{g} \: = \: \dfrac{3 \times 3 }{4 \times 2}}$

$: \longmapsto \: \sf{ _{w} \mu _{g} \: = \dfrac{9}{8} }$

$: \longmapsto \: \sf{ _{w} \mu _{g} \: = \: \cancel \dfrac{9}{8} }$

$: \longmapsto \: \underline{\boxed{\sf{ _{w} \mu _{g} \: = \: 1.125 }}}$