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Chapter 30: Problem 25

Total internal reflection occurs at an interface between plastic and air at incidence angles greater than \(37^{\circ} .\) Find the plastic's refractive index.

Short Answer

Expert verified
By calculating the right hand side of the equation in step 3, we find that the refractive index of the plastic is approximately 1.64.

Step by step solution

01

Identify given values

We're given that the critical angle for total internal reflection at the interface of plastic and air is \(37^{\circ}\). We also know that the refractive index of air is 1, since it is in comparison to the vacuum.
02

Apply Snell's Law

Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media, or equivalent to the reciprocal of the ratio of the indices of refraction. In the case of total internal reflection, the angle of refraction is \(90^{\circ}\). Therefore, applying Snell's Law, we have \( \sin(37^{\circ}) = \frac{1}{n}\), where \(n\) is the refractive index of the plastic we're trying to find.
03

Calculate the refractive index

Rearranging the equation from step 2 gives \( n = \frac{1}{\sin(37^{\circ})}\).

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Most popular questions from this chapter

At the aquarium where you work, a fish has gone missing in a 10-m-deep. 11-m-diameter cylindrical tank. You shine a flashlight in from the top edge of the tank, hoping to see if the missing fish is on the bottom. What's the smallest angle your flashlight beam can make with the horizontal if it's to illuminate the bottom?

Why is it usually inappropriate to consider low-frequency sound waves as traveling in rays? Why is the ray approximation more appropriate for high- frequency sound and for light?

In glass, which end of the visible spectrum has the smallest critical angle for total internal reflection?

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?

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