You can determine the index of refraction of a substance by determining its crit

Question

You can determine the index of refraction of a substance by determining its critical angle. (a) What is the index of refraction of a substance that has a critical angle of when submerged in water? What is the substance, based on Table 25.1? (b) What would the critical angle be for this substance in air?

Table 25.1 Mediumm Gases at 0G 1 atm Index of Refraction in Various Media Air Carbon dioxide Hydrogen Oxygen 1.000293 1.00045 1.000139 1.000271 Liquids at 20°c Benzene Carbon disulfide Carbon tetrachloride Ethanol Glycerine Water, fresh 1.501 1.628 1.461 1.361 1.473 1.333 Solids at 20°C 2.419 1.434 1.52 1.66 1.309 1.49 1.51 1.544 1.458 1.544 1.923 Diamond Fluorite Glass, crown Glass, flint Ice at 20°C Polystyrene Plexiglas crystalline Quartz, fused Sodium chloride Zircon

Explanation / Answer

from snells law

n1*sintheta1 = n2*sintheta2

n1 = refractive index of medium 1

n2 = refractive index of medium 2

theta1 = angle made by the light ray with the normal in medium 1

theta2 = angle made by the light ray with the normal in medium2

when the light undergoes internal reflection the refracted light ray im=n med 2 grazes along the interface making an angle in medium 2 = 90

part(a)

n1 = ?

n2 = 1.333

theta1 =

n1*sintheta1 = 1.333*sin90

n1 = 1.333/sintheta1

in the question theta1 is not given

substitute the value of theta1

part(b)

sintheta1 = 1.333/n1

theta1 = sin^-1(1.333/n1)

find the value n1 from part(a)

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