Light (frequency, wavelength etc.)

In summary, the conversation discussed estimating the distance of a vehicle with tail-lights appearing as a single orange/red blob on a dark road. The factors to consider in this estimation include the color of the tail-lights, the spatial separation of the lights, and the size of the pupil of a dark-adapted eye. The solution involves utilizing the material on single-slit diffraction and using the small-angle approximation to determine the relationship between the apex angle of a triangle formed by the two tail-lights and the distance to the eye.
  • #1
tim_3491
9
0

Homework Statement



Imagine that you are in a vehicle at night on a long straight road. There are no streetlights and one vehicle up ahead in the distance.
Estimate how far away the other vehicle would be for its tail-lights to appear as a single
orange/red blob.
In your answer, make quantitative estimates to characterise:
• the colour of the light emanating from the tail-lights
• the spatial separation of the tail-lights
• the size of the pupil of your dark-adapted eye.

Homework Equations





The Attempt at a Solution


red light has lambda = 700nm (700*10^-9m) but now i am not sure what to do. I need to equate/use lambda, lense of an eye and focal length/distance to car.
 
Physics news on Phys.org
  • #2
Have you had the material yet on single-slit diffraction? In this case, you will want to know the angular size of the "central maximum" for diffraction through a circular aperture (the size of the so-called Airy disk). The diameter of the dilated human pupil is about 2 cm. Draw a picture of the triangle formed by the two taillights and the location of your eye. You will want to use the "small-angle approximation" to find the relationship between the apex angle of that triangle, the separation of the lights, and the distance to your eye. The apex angle will equal the angular size of that central maximum when the taillights are at the "limit of resolution", which is the minimum distance at which you will see the two taillights as one light source.
 
  • #3


I would approach this problem by first considering the properties of light and how they relate to our perception. Light is an electromagnetic wave with a range of frequencies and wavelengths. The visible spectrum, which is the range of light that we can see, has wavelengths between approximately 400-700 nanometers (nm). Within this range, different wavelengths correspond to different colors, with shorter wavelengths appearing as blue and longer wavelengths appearing as red.

In this scenario, we are interested in the color of the tail-lights, which are emitting a single orange/red blob of light. This suggests that the tail-lights are emitting light with a wavelength of around 600-650nm, which falls within the red portion of the visible spectrum.

Next, we can consider the spatial separation of the tail-lights. The human eye has a limited ability to distinguish objects that are close together, known as resolution. The resolution of the human eye is dependent on several factors, including the size of the pupil. In a dark-adapted eye, the pupil can dilate to a maximum diameter of about 7mm. Using this information, we can estimate that the spatial separation of the tail-lights would need to be greater than 7mm for them to appear as a single blob to our eyes.

Finally, we can consider the distance to the other vehicle. The focal length of the eye, which is the distance between the lens and the retina, is approximately 17mm. Using this information, we can estimate that the other vehicle would need to be at least 17mm/7mm = 2.4 times further away than the spatial separation of the tail-lights for them to appear as a single blob.

In summary, to see the tail-lights of the other vehicle as a single orange/red blob, the light would need to have a wavelength of around 600-650nm, the spatial separation of the tail-lights would need to be greater than 7mm, and the other vehicle would need to be at least 2.4 times further away than the spatial separation of the tail-lights.
 

What is the difference between frequency and wavelength?

Frequency refers to the number of waves that pass through a certain point in one second, measured in Hertz (Hz). Wavelength, on the other hand, refers to the distance between two consecutive peaks or troughs of a wave, measured in meters (m). In simple terms, frequency is a measure of how often a wave occurs, while wavelength is a measure of the length of the wave.

How are frequency and wavelength related?

Frequency and wavelength are inversely proportional to each other. This means that as frequency increases, wavelength decreases and vice versa. This relationship is described by the equation: speed of light = frequency x wavelength. This means that as the speed of light is constant, if one of the values increases, the other must decrease to maintain the same speed.

Why is light sometimes described as a wave and other times as a particle?

Light exhibits properties of both a wave and a particle. This is known as the wave-particle duality of light. In certain experiments, light behaves like a wave, such as when it diffracts or interferes with itself. In other experiments, it behaves like a particle, such as when it transfers energy in discrete packets called photons. The behavior of light depends on the context and the type of experiment being conducted.

How is the color of light determined?

The color of light is determined by its frequency. The visible spectrum of light is made up of different colors, ranging from red (lowest frequency) to violet (highest frequency). When white light is passed through a prism, it separates into these different colors due to their varying frequencies. Other factors such as the intensity of light and the human eye's perception also play a role in how we perceive color.

Why do different materials have different colors?

The color of an object is determined by the wavelengths of light that it reflects or absorbs. When white light is shone on an object, certain wavelengths are absorbed by the object and others are reflected. The reflected wavelengths are what we perceive as color. Different materials have different atomic and molecular structures, which determine how they interact with light and which wavelengths they reflect or absorb. This is why different materials can have different colors.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
7K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Other Physics Topics
2
Replies
39
Views
3K
  • Classical Physics
Replies
21
Views
855
  • Introductory Physics Homework Help
Replies
1
Views
5K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
Back
Top