When a light ray travels from a denser medium (glass) to a rarer medium (air), how do its speed and wavelength

Question

When a light ray travels from a denser medium (glass) to a rarer medium (air), how do its speed and wavelength change?

Examoogle · Accepted Answer

The correct answer is Option A: Speed increases, wavelength increases. When light travels from a denser medium (higher refractive index) to a rarer medium (lower refractive index), its speed increases because the optical density is lower. Since the frequency of the light remains unchanged, the wavelength must increase to maintain the relationship $v = f \lambda$.

Step-by-Step Solution & Concepts:
When light travels from a denser medium (higher refractive index) to a rarer medium (lower refractive index), its speed increases because the optical density is lower. Since the frequency of the light remains unchanged, the wavelength must increase to maintain the relationship $v = f \lambda$.

Working Principle: The speed of light in a medium is given by $v = \frac{c}{n}$, where $c$ is the speed of light in a vacuum and $n$ is the refractive index. As light enters a rarer medium, $n$ decreases, causing $v$ to increase. Because the frequency ($f$) of light is determined by the source and remains constant across boundaries, the wavelength $\lambda$ must increase as $v$ increases according to $\lambda = \frac{v}{f}$.

Key Formulas: $v = f \lambda$ — Relationship between velocity, frequency, and wavelength; $n = \frac{c}{v}$ — Definition of refractive index; $\frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}$ — Ratio of velocities equals ratio of wavelengths

Key Points: Frequency of light is a property of the source and does not change when the medium changes.; The refractive index ($n$) is inversely proportional to the speed of light in that medium.; Light bends away from the normal when entering a rarer medium.

Applications: Refraction through lenses; Optical fiber communication; Mirage formation in deserts

Additional Info: Speed of light in vacuum ($c$) is approximately $3 	imes 10^8$ m/s.. Option B is incorrect because speed and wavelength increase, not decrease, when moving to a rarer medium.. Option C is incorrect because wavelength is directly proportional to speed when frequency is constant.

Answer: A is correct — The speed and wavelength of light both increase when passing from a denser to a rarer medium due to the decrease in optical refractive index.

Exam Tip: Always remember that 'Frequency never changes' during refraction, which is the key constraint for solving problems involving light speed and wavelength shifts.

Examoogle · Answer

Option B: Speed decreases, wavelength decreases

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Option C: Speed increases, wavelength remains constant

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Option D: Speed remains constant, wavelength decreases

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