Question

Which of the following interface combinations has the smallest critical angle? a) light traveling from ice to diamond b) light traveling from quartz to Lucite c) light traveling from diamond to glass d) light traveling from Lucite to diamond e) light traveling from Lucite to quartz

Short answer

Answer: The interface combination with the smallest critical angle is light traveling from ice to diamond (option a).

Step-by-step solution

List the index of refraction for each medium

First, let's find the refractive indices for each medium. n(ice) = 1.31 n(diamond) = 2.42 n(quartz) = 1.544 n(Lucite) = 1.495 n(glass) = 1.5

Calculate the ratios of indices for each interface combination

Now, we will calculate the ratio of the refractive indices for each interface combination. a) ice to diamond: \(\frac{n_{diamond}}{n_{ice}} = \frac{2.42}{1.31} = 1.847\) b) quartz to Lucite: \(\frac{n_{Lucite}}{n_{quartz}} = \frac{1.495}{1.544} = 0.968\) c) diamond to glass: \(\frac{n_{glass}}{n_{diamond}} = \frac{1.5}{2.42} = 0.619\) d) Lucite to diamond: \(\frac{n_{diamond}}{n_{Lucite}} = \frac{2.42}{1.495} = 1.617\) e) Lucite to quartz: \(\frac{n_{quartz}}{n_{Lucite}} = \frac{1.544}{1.495} = 1.032\)

Compare the ratios to find the smallest critical angle

We can now compare the ratios we calculated in Step 2 to determine which interface combination has the smallest critical angle. The combination with the largest ratio of refractive indices will have the smallest critical angle. In this case, the combination with the largest ratio is: a) ice to diamond: 1.847 Therefore, the interface combination with the smallest critical angle is light traveling from ice to diamond (option a).