Final answer:
For reflected light, the speed and wavelength remain the same as the incident light, but for refracted light in water, the speed becomes 2.25 × 10⁸ m/s and the wavelength becomes 442.86 nm, with the frequency staying unchanged at approximately 5.09 × 10⁸ Hz.
Step-by-step explanation:
When monochromatic light with a wavelength of 589 nm passes from air into water, the speed and wavelength of light change, but the frequency remains constant because frequency depends only on the source of the light. The index of refraction of water (1.33) affects the speed and wavelength of the light within the medium.
The speed of light in water is given by c/n, where c is the speed of light in vacuum (approximately 3.00 × 108 m/s) and n is the refractive index. Therefore, the speed of light in water equals 2.25 × 108 m/s. The wavelength of light in water (λwater) can be found using the formula λwater = λair / n, which gives us a wavelength of 442.86 nm (589 / 1.33).
The frequency (f) of light remains unchanged during reflection or refraction, as frequency is only determined by the source. The frequency can be calculated from the speed of light in the vacuum (c) and the wavelength in the air (λair) using the formula f = c / λair. Therefore, the frequency is approximately 5.09 × 1014 Hz.
For (1) reflected light, both the speed and wavelength remain unchanged, while for (2) refracted light, the speed is 2.25 × 108 m/s, the wavelength is 442.86 nm, but the frequency remains constant at approximately 5.09 × 1014 Hz.