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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 angle for light propagating in glass when the glass is immersed in water is approx. \(61.04\) degrees, in benzene is approx. \(78.46\) degrees, but there is no critical angle for diiodomethane due to its higher refractive index.

Step by step solution

01

Identify given values

First thing is to identify the known values. The refractive index of glass (\(n_1\)) is given as \(1.52\). The refractive indices of water (\(n_2\)), benzene (\(n_2\)), and diiodomethane (\(n_2\)) are approximately \(1.33\), \(1.50\), and \(1.74\) respectively.
02

Apply Snell's law formula

Now, you will use the formula \(\sin(\theta_c) = n_2/n_1\) to find the critical angles for each scenario. Rewriting the formula for \(\theta_c\), we get \(\theta_c = \arcsin(n_2/n_1)\).
03

Calculate the critical angle when glass is immersed in water

Substitute \(n_2=1.33\) and \(n_1=1.52\) in the above formula to calculate the critical angle when glass is immersed in water. \(\theta_c = \arcsin(1.33/1.52)\). After calculation, the critical angle will be approx. \(61.04\) degrees.
04

Calculate the critical angle when glass is immersed in benzene

Repeat as in step 3, but now \(n_2=1.50\). \(\theta_c = \arcsin(1.50/1.52)\). The result should be approx. \(78.46\) degrees.
05

Calculate the critical angle when glass is immersed in diiodomethane

Now, repeat as in steps 3 and 4, but with \(n_2=1.74\). Note, since \(n_2>n_1\), there is no critical angle. Total internal reflection cannot occur when light travels from a denser medium (like glass) to a less dense medium (like diiodomethane).

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