Given small samples of three liquids, you are asked to determine their refractiv

Question

Given small samples of three liquids, you are asked to determine their refractive indexes. However, you do not have enough of each liquid to measure the angle of refraction for light refracting from air into the liquid. Instead, for each liquid, you take a rectangular block of glass (n= 1.52) and place a drop of the liquid on the top surface of the block. You shine a laser beam with wavelength 638 nm in vacuum at one side of the block and measure the largest angle of incidence for which there is total internal reflection at the interface between the glass and the liquid (Figure 1). Your results are given in the table (Figure 2). What is the refractive index of liquid A at this wavelength? What is the refractive index of liquid B at this wavelength? What is the refractive index of liquid C at this wavelength?

Explanation / Answer

A) to find incidence angle at liquid-glass surafce

1 x sin52 = 1.52 x sin @

@ = 31.23 deg

so incidence angle for glass-liquid surafce i = 90 -@ =58.77 deg

for internal reflection using snell's Law,

ni sini = nr sinr

for internal reflection nr = 90 deg

1.52 x sin58.77 = nr sin90

nr =1.30

B)
to find incidence angle at liquid-glass surafce

1 x sin44.3 = 1.52 x sin @

@ = 37.35 deg

so incidence angle for glass-liquid surafce i = 90 -@ =62.65 deg

for internal reflection using snell's Law,

ni sini = nr sinr

for internal reflection nr = 90 deg

1.52 x sin62.65 = nr sin90

nr =1.35

C) to find incidence angle at liquid-glass surafce

1 x sin36.3 = 1.52 x sin @

@ = 22.92 deg

so incidence angle for glass-liquid surafce i = 90 -@ =67.08 deg

for internal reflection using snell's Law,

ni sini = nr sinr

for internal reflection nr = 90 deg

1.52 x sin67.08 = nr sin90

nr =1.40

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