What Remains Unchanged When Light Waves Enter Water from Air?

Correct Answer: (C) Frequency

Understanding What Happens When Light Enters Water from Air

When a light wavlight enters water from aire passes from air into water, it crosses the boundary between two media having different optical properties. Air is an optically rarer medium, while water is an optically denser medium. As a result, several properties of the light wave change at the interface.

The speed of light decreases when it enters water from air. Since the frequency of light is determined by the source producing the wave, the frequency cannot suddenly change at the boundary. Therefore, the decrease in the speed of light is accompanied by a decrease in its wavelength.

The only property among the given options that remains unchanged during this transition is the frequency of light. Therefore, Option (C) is correct.

Why Does the Frequency of Light Remain Unchanged?

The frequency of a light wave is determined by the source that produces the light. When the wave enters another transparent medium, the source does not change. Therefore, the rate at which wave oscillations arrive at the boundary must remain continuous.

If the frequency were different on the two sides of the boundary, successive wave crests would accumulate or disappear at the interface. Such a discontinuity does not occur in the steady propagation of light. Therefore, the frequency remains the same in air and water.

Hence:

Frequency in air = Frequency in water

Although the frequency remains unchanged, the speed and wavelength adjust according to the optical properties of the new medium.

Relation Between Speed, Frequency, and Wavelength

The fundamental wave relation is:

v = fλ

where v is the speed of the wave in the medium, f is the frequency, and λ is the wavelength.

When light enters water from air, its speed decreases because water has a higher refractive index than air. Since the frequency remains constant, the wavelength must also decrease to satisfy the wave relation.

Therefore:

Speed decreases → Frequency remains constant → Wavelength decreases

Change in the Speed of Light in Water

The speed of light in a medium is related to its refractive index by:

v = c/n

where c is the speed of light in vacuum, n is the refractive index of the medium, and v is the speed of light in that medium.

Water has a greater refractive index than air. Therefore, light travels more slowly in water than in air. This reduction in speed is responsible for the corresponding reduction in wavelength.

Detailed Analysis of Each Option

Option (A): Wavelength

Option (A) is incorrect. The wavelength of light does not remain unchanged when light enters water from air. The speed of light decreases in water, while its frequency remains constant.

From the relation v = fλ, if the speed decreases while the frequency remains unchanged, the wavelength must decrease. Therefore, the wavelength of light in water is smaller than its wavelength in air.

Option (B): Wavenumber

Option (B) is incorrect. Wavenumber is inversely related to wavelength. It is commonly expressed as:

Wavenumber = 1/λ

Since the wavelength of light decreases when it enters water from air, the wavenumber increases. Therefore, wavenumber does not remain unchanged.

Option (C): Frequency

Option (C) is correct. The frequency of light is determined by the source and remains unchanged when light passes from one transparent medium into another.

Although the speed and wavelength change at the air-water interface, the number of oscillations per second remains the same. Therefore, the frequency of light in water is equal to its frequency in air.

Option (D): Intensity

Option (D) is incorrect. The intensity of light generally does not remain unchanged when light crosses the boundary between air and water. At the interface, a portion of the incident light may be reflected while the remaining portion is transmitted into the water.

Because some energy can be carried away by the reflected wave, the intensity of the transmitted light is generally different from the intensity of the incident light. Therefore, intensity cannot be considered the unchanged quantity in this question.

How Wavelength Changes When Light Enters Water

The wavelength of light in a medium is related to its wavelength in air or vacuum through the refractive index. Since the speed of light decreases in water while frequency remains constant, the wavelength also becomes shorter.

If the refractive index of water is represented by n, then approximately:

λ_water = λ_air/n

Since the refractive index of water is greater than 1, the wavelength in water is smaller than the wavelength in air. This confirms that wavelength is not the correct answer.

How Wavenumber Changes in Water

Wavenumber represents the number of wavelengths present per unit distance and is inversely proportional to wavelength. Since the wavelength decreases when light enters water, more wave cycles fit into a given distance.

Therefore, the wavenumber increases in water. This means that wavelength and wavenumber both change during the transition, but in opposite ways: wavelength decreases while wavenumber increases.

Physical Interpretation of Frequency Conservation

Consider a continuous train of light waves reaching the air-water boundary. The number of wave crests arriving at the boundary every second must equal the number of wave crests entering the water every second. Therefore, the frequency cannot change at the interface.

Inside water, the wave travels more slowly. Because the same number of oscillations must pass per second, the distance between successive wave crests becomes smaller. This reduced distance between wave crests is the shorter wavelength of light in water.

Summary of Changes in Light Wave Properties

When light travels from air into water, its speed decreases because water is optically denser than air. The frequency remains unchanged because it is determined by the source. As a consequence of the lower speed and unchanged frequency, the wavelength decreases.

Since wavenumber is inversely proportional to wavelength, the wavenumber increases. The intensity may also change because a fraction of the incident light can be reflected at the boundary.

Therefore, among wavelength, wavenumber, frequency, and intensity, only frequency remains unchanged.

Final Answer

The frequency of light remains unchanged when light waves enter water from air. Therefore, the correct answer is Option (C).

Conclusion

When light enters water from air, the optical medium changes, causing the speed and wavelength of the light to decrease. The wavenumber increases because it is inversely proportional to wavelength, and the intensity can change due to partial reflection at the interface. However, the frequency is fixed by the source and remains unchanged during the transition. Hence, Option (C) Frequency is the correct answer.