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Chapter 30: Problem 24

What is the critical angle for light propagating in glass with \(n=1.52\) when the glass is immersed in (a) water, (b) benzene, and (c) diiodomethane?

Short Answer

Expert verified
The critical angles for light moving from glass to water, benzene and diiodomethane can be calculated as follows: For water, it is the inverse sin of the ratio 1.33/1.52; for benzene, it is the inverse sin of the ratio 1.50/1.52; for diiodomethane, there is no real critical angle since its refractive index is greater than that of glass.

Step by step solution

01

Determine the refractive indices

First, check the known refractive indices for each of the three substances mentioned in the exercise. The relevant values are approximately 1.33 for water, 1.50 for benzene, and 1.74 for diiodomethane.
02

Calculate for water

Then, apply the formula for the critical angle when light is moving from glass to water. Critical angle \(C_{g-w}\) can be calculated as \(C_{g-w} = \sin^{-1}(n_{water}/n_{glass}) = \sin^{-1}(1.33/1.52)\). Compute the inverse sine of the ratio to get the result in degrees.
03

Calculate for benzene

Next, using the same method for benzene, we have \(C_{g-b} = \sin^{-1}(n_{benzene}/n_{glass}) = \sin^{-1}(1.50/1.52)\). Again the inverse sine of the ratio gives the result in degrees.
04

Calculate for diiodomethane

Lastly, plug in the values for diiodomethane in the formula \(C_{g-d} = \sin^{-1}(n_{diiodomethane}/n_{glass}) = \sin^{-1}(1.74/1.52)\). Note that since the refractive index of diiodomethane is greater than that of glass, there will not be a real critical angle, indicating total internal reflection does not occur when the light is moving from glass to diiodomethane.

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