When light enters from air into water, how do the frequency and wavelength of the light change in the water compared with in the air?

Introduction / Context:
When light passes from one medium to another, such as from air to water, its speed changes due to the different optical densities of the media. Students often wonder what happens to the frequency and wavelength in this process. This question tests your understanding of how these quantities are related by the wave equation and which ones remain constant at a boundary between two media.

Given Data / Assumptions:
- Light is initially travelling in air and then enters water.
- Water is optically denser than air, so the speed of light in water is less than in air.
- Options describe possible changes in frequency and wavelength.

Concept / Approach:
The basic wave relation is v = f * lambda, where v is speed, f is frequency and lambda is wavelength. At the boundary between two media, the frequency of light remains unchanged because it is determined by the source of the light. However, the speed changes depending on the refractive index of the medium. In water, the speed of light is lower than in air, so to keep the product f * lambda equal to the new speed, the wavelength must decrease. Therefore, frequency stays the same, speed decreases and wavelength becomes smaller in water than in air.

Step-by-Step Solution:
Step 1: Recall the relation v = f * lambda for a wave. Step 2: At a boundary, the frequency f is determined by the source and does not change when light enters a different medium. Step 3: When light enters water from air, its speed v decreases because water is optically denser. Step 4: Since v decreases and f remains constant, the wavelength lambda must decrease to satisfy v = f * lambda. Step 5: Therefore, frequency is unchanged, but the wavelength is smaller in water than in air.

Verification / Alternative check:
Consider numerical values: take light with frequency f. In air, speed v_air is about 3 * 10^8 m/s and wavelength lambda_air = v_air / f. In water, speed v_water is about 2.25 * 10^8 m/s, so lambda_water = v_water / f, which is smaller than lambda_air because v_water is smaller while f is the same. This confirms that the wavelength must decrease when light enters water from air.

Why Other Options Are Wrong:
Frequency increases and speed decreases: Frequency remains unchanged; it is not increased by entering a new medium.
Frequency is same but the wavelength is larger in water than in air: This would require speed to increase, but in reality light slows down in water, so wavelength cannot increase.
Frequency and speed both decreases: The speed decreases, but frequency remains constant at the boundary, so this joint change is incorrect.

Common Pitfalls:
Some students incorrectly think that all three quantities (speed, frequency and wavelength) change when light enters a new medium. Others think that wavelength must stay fixed because they associate it with "colour". In reality, the perceived colour relates mainly to frequency, which remains constant, while wavelength adjusts according to the medium's refractive index. Remembering that the source fixes the frequency while the medium affects speed helps avoid these misunderstandings.

Final Answer:
When light enters water from air, the frequency remains the same but the wavelength becomes smaller in water than in air.