A layer of benzene (n=1.50) 2.60 cm deep floats on water (n=1.33) that is 6.50cm deep. What is the apparent distance from the upper benzene surface to the bottom of the water layer when it is viewed at normal incidence? Please explain.
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Consider refraction through the water layer (layer 2) into the benzene layer (layer 3) first (Please see the attached diagram). Further assume air to be the layer 1.
OT is the real depth, after refraction through the water layer.
PT is the apparent depth after refraction through the water layer into the benzene layer.
We know that,
Refractive index n = Real depth/Apparent depth
`n = (OT)/(PT)`
`rArr 0.886667 = 6.5/(PT)`
`PT = 6.5/0.886667=7.33` cm
Now consider refraction through the benzene layer into the air.
PW is the real depth, after refraction through the benzene layer.
QW is the apparent depth after refraction through the benzene layer into the air.
Plugging in the values in this case,
`1.5 = (PW)/(QW)`
`rArr QW = (PW)/1.5`
`=(7.33+2.6)/1.5 ` cm
`= 6.62 ` cm (when viewed from normal incidence).
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