Question

The wavelength of light changes as light goes from one medium to another, while the frequency remains the same. Is the wavelength longer or shorter in water than in air? Explain in terms of the equation speed 5 frequency 3 wavelength.

A certain orange light has a wavelength of 600 nm (6 3 1027 m) in air. What is its wavelength in water, where light travels at 75% of its speed in air? In Plexiglas, where light travels at 67% of its speed in air?

Answer 1

The wavelength of light is longer in water and Plexiglas compared to air. In water, the wavelength is calculated by dividing the speed of light in air by 0.75, while in Plexiglas, it is calculated by dividing the speed of light in air by 0.67.

Step-by-step explanation:

When light goes from one medium to another, such as from air to water, its wavelength changes while the frequency remains the same. The equation that relates speed, frequency, and wavelength is v = fλ, where v is the speed of light in the medium, f is the frequency, and λ is the wavelength. In water, light travels at 75% of its speed in air, so the wavelength in water would be longer than in air. Similarly, in Plexiglas, light travels at 67% of its speed in air, so the wavelength in Plexiglas would be even longer than in water.

To find the wavelength in water, we can use the equation v = fλ. Given that the wavelength in air is 600 nm (6.3 x 10^(-7) m), and the speed of light in water is 75% of its speed in air, we can calculate the wavelength in water by dividing the speed of light in air by 75% (or 0.75). This gives us:

(3 x 10^8 m/s) / 0.75 = 4 x 10^8 m/s

Therefore, the wavelength in water is 4 x 10^8 m/s divided by the frequency.

To find the wavelength in Plexiglas, we can use the same equation with the speed of light in Plexiglas (67% of its speed in air). Given the wavelength in air and the speed of light in Plexiglas, we can calculate the wavelength in Plexiglas using the equation:

(3 x 10^8 m/s) / 0.67 = 4.48 x 10^8 m/s

Therefore, the wavelength in Plexiglas is 4.48 x 10^8 m/s divided by the frequency.

Answer 2

λw = 450 nm

λg = 402 nm

Step-by-step explanation:

Frequency of a wave is defined as the number of vibrations coming out of the source in one second.

The frequency of a wave is the fundamental property of the source.

The relation among the wavelength, wave velocity and frequency is given by

wave velocity = frequency x wavelength

Frequency is constant while the velocity and wavelength changes.

wavelength in air, λa = 600 nm

Let the wavelength in water is λw.

speed of light in air, c = 3 x 10^8 m/s

speed of light in water = 75 % of c = 0.75 x 3 x 10^8 = 2.25 x 10^8 m/s

speed of light in plexglass = 67 % of c = 0.67 x 3 x 10^8 = 2.01 x 10^8 m/s

`(\lambda _(w))/(\lambda _(a))=(velocity in water)/(velocity in light )`

`\lambda _(w)=600* (2.25* 10^(8))/(3* 10^(8))`

λw = 450 nm

`(\lambda _(g))/(\lambda _(a))=(velocity in glass)/(velocity in light )`

`\lambda _(g)=600* (2.01* 10^(8))/(3* 10^(8))`

λg = 402 nm