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Ch 35: Optical Instruments
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 35: Optical InstrumentsProblem 21
Chapter 35, Problem 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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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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