A light ray travels from a medium with refractive index 1.5 to a medium with refractive index 1.33. How do the

Question

A light ray travels from a medium with refractive index 1.5 to a medium with refractive index 1.33. How do the speed and wavelength of the light change as it enters the second medium?

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The correct answer is Option A: Speed increases, wavelength increases. When light travels from a denser medium ($n_1 = 1.5$) to a rarer medium ($n_2 = 1.33$), its speed increases as the optical resistance decreases. Since frequency ($f$) remains constant during refraction, the relationship $v = f \lambda$ dictates that wavelength ($\lambda$) must also increase.

Step-by-Step Solution & Concepts:
When light travels from a denser medium ($n_1 = 1.5$) to a rarer medium ($n_2 = 1.33$), its speed increases as the optical resistance decreases. Since frequency ($f$) remains constant during refraction, the relationship $v = f \lambda$ dictates that wavelength ($\lambda$) must also increase.

Working Principle: The refractive index ($n$) is defined as the ratio of speed of light in vacuum ($c$) to speed in the medium ($v$), expressed as $n = \frac{c}{v}$. As the medium changes from high to low refractive index, the speed $v$ increases. Because the frequency is determined by the source and does not change when moving between media, the wavelength $\lambda = \frac{v}{f}$ must increase proportionally with speed.

Key Formulas: $n = \frac{c}{v}$ — definition of refractive index; $v = f \lambda$ — relation between speed, frequency, and wavelength

Key Points: Frequency of light is a property of the source and remains constant across all media.; Refractive index is inversely proportional to the speed of light in that medium.; Bending of light (refraction) occurs because of the change in speed when entering a medium with a different optical density.

Advantages: Explains phenomena like mirages and the apparent depth of water bodies.

Applications: Design of lenses for optical instruments; Fiber optic communication systems

Additional Info: The refractive index of vacuum is 1, air is approximately 1.0003, and water is 1.33.. Option B, C, and D are incorrect because they imply inconsistent relationships between wave properties defined by $v = f \lambda$.

Answer: A is correct — Speed and wavelength increase when light travels from a denser medium to a rarer medium because the optical density is lower.

Exam Tip: Always remember that during refraction, frequency is the only property of a wave that NEVER changes; use this as your anchor when analyzing changes in $v$ or $\lambda$.

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Option B: Speed increases, wavelength decreases

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Option C: Speed decreases, wavelength increases

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Option D: Speed decreases, wavelength decreases

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