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Chapter 20: Q19P (page 526)

The photograph of upconversion in Color Plate 21shows total internal reflection of the blue ray inside the cuvet. The angle of incidence of the blue ray on the wall of the cuvet is~55°. We estimate that the refractive index of the organic solvent is 1.50and the refractive index of the fused-silicacuvet is 1.46. Calculate the critical angle for total internal reflection at the solvent/ silica interface and at the silica/air interface. From your calculation, which interface is responsible for total internal reflection in the photo?

Short Answer

Expert verified

The critical angle for total internal refractive index is θcritical=76.7°θcritical=43.6°.

Step by step solution

01

Concept used.

The following formula may be used to calculate the critical angle for total internal reflection:sinθcritical=n2n1

02

The critical angle.

The critical angle for the solvent/silica interaction is:

sinθcritical=1.461.5sinθcritical=0.9733θcritical=76.7°

The critical angle for the silica/air interaction is:

sinθcritical=11.45sinθcritical=0.6897θcritical=43.6°

The angle of incidence of the blue ray on the wall of the cuvet is55°.Which is a smaller angle than the critical angle for the solvent/silica contact and a bigger angle than the critical angle for silica/air. As a result, the photo's whole internal reflection is caused by the silica/air contact.

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Most popular questions from this chapter

Light passes from benzene (medium1)to water (medium 2) in Figure 20at (a)θ1=30°or (b)θ1=0°. Find the angleθ2in each case.

The variation of refractive index, n, with wavelength for fused silica is given by

n2‐1=(0.6961663)λ2λ2‐(0.0684043)2+(0.4079426)λ2λ2‐(0.1162414)2+(0.8974794)λ2λ2‐(9.896161)2

where λ is expressed in μm.

(a) Make a graph of n versus λ with points at the following wavelengths: 0.2,0.4,0.6,0.8,1,2,3,4,5, and 6μm.

(b) The ability of a prism to spread apart (disperse) neighboring wavelengths increases as the slope dn/dλincreases. Is the dispersion of fused silica greater for blue light or red light?

Explain how beam chopping reduces line noise and noise from source drift.

Here is an extremely sensitive method for measuring nitrite () down to in natural waters. The water sample is treated with sulfanilamide and N-(1-naphthylethylenediamine) in acid solution to produce a colored product with a molar absorptivity of 4.5×104M-1cm-1at 540 nm. The colored solution is pumped into a 4.5-meter-long, coiled Teflon tube whose fluorocarbon wall has a refractive index of 1.29. The aqueous solution inside the tube has a refractive index near 1.33. The colored solution is pumped through the coiled tube. An optical fiber delivers white light into one end of the tube, and an optical fiber at the other end leads to a polychromator and detector.

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The prism shown here is used to totally reflect light at a90°angle. No surface of this prism is silvered. Use Snell's law to explain why total reflection occurs. What is the minimum refractive index of the prism for total reflection?
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