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Chapter 1: Problem 49

At what minimum angle will you get total internal reflection of light traveling in water and reflected from ice?

Short Answer

Expert verified
The minimum angle at which total internal reflection occurs for light traveling from water to ice is approximately \(80.57°\).

Step by step solution

01

Gather information about refractive indices of materials involved

We need the refractive indices of water and ice. The refractive index (n) of a medium shows how much it can bend light. The refractive indices of water and ice are 1.33 and 1.31, respectively. We will use these values in Snell's law.
02

Determine the critical angle using the formula and Snell's law

The critical angle (\(θ_c\)) is the angle of incidence in the denser medium (water, in this case) for which the angle of refraction in the less dense medium (ice) is 90 degrees. The critical angle can be found using Snell's law: \[n_1 \times sin(θ_1) = n_2 \times sin(θ_2)\] Since the angle of refraction (\(θ_2\)) in the less dense medium (ice) is 90 degrees, it becomes: \[n_{water} \times sin(θ_c) = n_{ice} \times sin(90)\]
03

Solve for the critical angle

Substitute the values of the refractive indices into the equation: \[1.33 \times sin(θ_c) = 1.31 \times sin(90)\] We can simplify the equation as: \[sin(θ_c) = \frac{1.31}{1.33}\] Now, we find the value of the critical angle: \[θ_c = sin^{-1}(\frac{1.31}{1.33})\] Using a calculator, we get: \[θ_c ≈ 80.57°\]
04

Report the minimum angle for total internal reflection

The minimum angle at which total internal reflection occurs for light traveling from water to ice is approximately 80.57 degrees.

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Most popular questions from this chapter

Verify that the critical angle for light going from water to air is \(48.6^{\circ},\) as discussed at the end of Example 1.4 regarding the critical angle for light traveling in a polystyrene (a type of plastic) pipe surrounded by air.

Suppose you are using total internal reflection to make an efficient corner reflector. If there is air outside and the incident angle is \(45.0^{\circ},\) what must be the minimum index of refraction of the material from which the reflector is made?

When light is reflected at Brewster's angle from a smooth surface, it is \(100 \%\) polarized parallel to the surface. Part of the light will be refracted into the surface. Describe how you would do an experiment to determine the polarization of the refracted light. What direction would you expect the polarization to have and would you expect it to be \(100 \%\) ?

When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to \(\frac{1}{\lambda} .\) Does this mean there is more scattering for small \(\lambda\) than large \(\lambda\) ? How does this relate to the fact that the sky is blue?

Does the fact that the light flash from lightning reaches you before its sound prove that the speed of light is extremely large or simply that it is greater than the speed of sound? Discuss how you could use this effect to get an estimate of the speed of light.
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