Question 34.3: Angle of Refraction for Glass A light ray of wavelength 589 ...
Angle of Refraction for Glass
A light ray of wavelength 589 nm traveling through air is incident on a smooth, flat slab of crown glass at an angle of 30.0° to the normal.
(A) Find the angle of refraction.
(B) Find the speed of this light once it enters the glass.
(C) What is the wavelength of this light in the glass?
(A) Conceptualize Study Figure 34.11a, which illustrates the refraction process occurring in this problem. We expect that \theta_2<\theta_1 because the speed of light is lower in the glass.
Categorize This is a typical problem in which we apply the wave under refraction model.
Analyze Rearrange Snell’s law of refraction to find \sin \theta_2:
\sin \theta_2=\frac{n_1}{n_2} \sin \theta_1Solve for \theta_2 :
\theta_2=\sin ^{-1}\left(\frac{n_1}{n_2} \sin \theta_1\right)Substitute indices of refraction from Table 34.1 and the incident angle:
\theta_2=\sin ^{-1}\left(\frac{1.00}{1.52} \sin 30.0^{\circ}\right)=19.2^{\circ}(B) Solve Equation 34.3 for the speed of light in the glass:
n \equiv \frac{\text { speed of light in vacuum }}{\text { speed of light in a medium }} \equiv \frac{c}{v} (34.3)
v=\frac{c}{n}Substitute numerical values:
v=\frac{3.00 \times 10^8 m/s}{1.52}=1.97 \times 10^8 m/s(C) Use Equation 34.6 to find the wavelength in the glass:
n=\frac{\lambda}{\lambda_n} (34.6)
\lambda_n=\frac{\lambda}{n}=\frac{589 nm}{1.52}=388 nmFinalize In part (A), note that \theta_2<\theta_1, consistent with the slower speed of the light found in part (B). In part (C), we see that the wavelength of the light is shorter in the glass than in the air.
| Table 34.1 Indices of Refraction | |||
| Substance | Index of Refraction |
Substance | Index of Refraction |
| Solids at 20°C | Liquids at 20°C | ||
| Cubic zirconia | 2.20 | Benzene | 1.501 |
| Diamond (C) | 2.419 | Carbon disulfide | 1.628 |
| Fluorite (CaF_2) | 1.434 | Carbon tetrachloride | 1.461 |
| Fused quartz (SiO_2) | 1.458 | Ethyl alcohol | 1.361 |
| Gallium phosphide | 3.50 | Glycerin | 1.473 |
| Glass, crown | 1.52 | Water | 1.333 |
| Glass, flint | 1.66 | ||
| Ice (H_2O) | 1.309 | Gases at 0°C, 1 atm | |
| Polystyrene | 1.49 | Air | 1.000 293 |
| Sodium chloride (NaCl) | 1.544 | Carbon dioxide | 1.000 45 |
| Note: All values are for light having a wavelength of 589 nm in vacuum. | |||
