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Ch 35: Optical Instruments
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 35: Optical InstrumentsProblema 21
Capitolo 35, Problema 21

A sheet of glass has nred = 1.52 and nviolet = 1.55. A narrow beam of white light is incident on the glass at 30°. What is the angular spread of the light inside the glass?

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Determine the relationship between the angle of refraction and the angle of incidence using Snell's Law: \( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \), where \( n_1 \) is the refractive index of the medium the light is coming from (air, \( n_1 = 1.00 \)), \( \theta_1 \) is the angle of incidence, \( n_2 \) is the refractive index of the glass, and \( \theta_2 \) is the angle of refraction.
Apply Snell's Law for red light (\( n_{red} = 1.52 \)) to find the angle of refraction for red light: \( \sin(\theta_{red}) = \frac{n_1 \sin(\theta_1)}{n_{red}} \). Substitute \( \theta_1 = 30° \) and solve for \( \theta_{red} \).
Repeat the process for violet light (\( n_{violet} = 1.55 \)) using Snell's Law: \( \sin(\theta_{violet}) = \frac{n_1 \sin(\theta_1)}{n_{violet}} \). Substitute \( \theta_1 = 30° \) and solve for \( \theta_{violet} \).
Calculate the angular spread of the light inside the glass by finding the difference between the angles of refraction for red and violet light: \( \Delta\theta = \theta_{red} - \theta_{violet} \).
Express the angular spread \( \Delta\theta \) in degrees, ensuring that the result reflects the difference in the refractive behavior of red and violet light within the glass.

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Refraction

Refraction is the bending of light as it passes from one medium to another with different optical densities. This phenomenon occurs due to a change in the speed of light in different materials, described by Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two media.
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Index of Refraction

Index of Refraction

The index of refraction (n) is a dimensionless number that describes how much light slows down in a medium compared to its speed in a vacuum. In this case, n<sub>red</sub> = 1.52 and n<sub>violet</sub> = 1.55 indicate that violet light travels slower in glass than red light, leading to different angles of refraction for each color.
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Index of Refraction

Angular Spread

Angular spread refers to the range of angles at which different wavelengths of light are refracted when passing through a medium. In this scenario, the difference in indices of refraction for red and violet light will cause them to bend at different angles, resulting in a spread of colors within the beam as it travels through the glass.
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Conservation of Angular Momentum
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