A sheet of glass has n_red = 1.52 and n_violet = 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?

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Refraction

Index of Refraction

Angular Spread

A sheet of glass has n_red = 1.52 and n_violet = 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?