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Difficulty: MediumWaves, Sound, and Light

A monochromatic beam of light travels through air and enters a transparent block of crown glass. As the light wave enters the optically denser glass medium, what happens to its speed, wavelength, and frequency?

  1. A
    Its speed increases and its frequency decreases, while its wavelength remains constant.
  2. B
    Its speed decreases and its frequency decreases, while its wavelength remains constant.
  3. Its speed decreases and its wavelength decreases, while its frequency remains constant.Answer
  4. D
    Its speed increases and its wavelength increases, while its frequency remains constant.

Answer

Its speed decreases and its wavelength decreases, while its frequency remains constant.
When light transitions from air into a medium with a higher refractive index such as glass, its propagation speed decreases (v=c/nv = c/n). The frequency of the oscillation is an intrinsic property established by the wave source and remains invariant at the interface. By the wave relationship v=fλv = f\lambda, a reduction in wave velocity at constant frequency results in a proportional reduction in wavelength.

Step-by-Step Solution

1
Determine the effect of the medium change on wave speed.
The speed of light decreases from c≈3.0×108 m/sc \approx 3.0 \times 10^8\text{ m/s} in air to approximately 2.0×108 m/s2.0 \times 10^8\text{ m/s} in crown glass (n≈1.52n \approx 1.52) based on v=cnv = \frac{c}{n}.
An increase in optical density (higher index of refraction) reduces the propagation speed of electromagnetic waves.
2
Determine the behavior of wave frequency across the medium boundary.
The frequency (ff) remains completely unchanged.
Wave frequency is set solely by the emitting source and is conserved across media boundaries because the number of wave cycles arriving per second must equal the number transmitted.
3
Apply the wave equation to determine the resulting change in wavelength.
The wavelength (λ\lambda) decreases proportionally with speed according to λ=vf\lambda = \frac{v}{f}.
With speed vv reduced and frequency ff constant, the spatial distance between consecutive crests must shorten.

Key Concept

Wave speed and wavelength changes during medium transition under constant frequency (v=fλv = f\lambda).
Estimated Time:45s
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Topics

Waves, Sound, and Light

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