Diffraction related to Resolving Power

In summary, the conversation discusses the calculation of the wavelength of light emitted by a car's taillights based on the distance between the taillights and the observer's eye diameter. The attempt at a solution yielded a result in the visible range, but not a typical color for tail lights. It is recommended to include the effect of the index of refraction for a more accurate answer.
  • #1
wizzleman
5
0

Homework Statement



A car passes you on the highway and you notice the taillights of the car are 1.22 m apart. Assume that the pupils of your eyes have a diameter of 7.1 mm and index of refraction of 1.36. Given that the car is 14.1 km away when the taillights appear to merge into a single spot of light because of the effects of diffraction, what wavelength of light does the car emit from its taillights (what would the wavelength be in vacuum)?

Homework Equations



I tried using

d=(1.22λy)/D

where d = 1.22m, D = 7.1mm, y=14.1km

The Attempt at a Solution



I got 5.035x10^-7 as my answer but SmartPhysics keeps on saying that I'm off by a power of ten and I've cycled between negative options but I can't get the answer.
 
Physics news on Phys.org
  • #2
Hello.

A couple of things seem odd. If you changed your answer by a power of 10, the wavelength would no longer be in the visible portion of the spectrum.

Your answer is in the visible range, but it corresponds to a bluish-green color (odd for tail lights). See http://www.gamonline.com/catalog/colortheory/visible.php

If you include the effect of the index of refraction, I think you'll get an answer that's much more realistic for tail lights.
 

1. What is diffraction and how does it relate to resolving power?

Diffraction is the bending of waves around obstacles or through openings. In terms of resolving power, diffraction occurs when light waves pass through a narrow slit or aperture, causing them to spread out and interfere with each other. This interference can affect the ability to distinguish between two closely spaced objects, ultimately impacting the resolving power of a system.

2. How does the size of the slit or aperture affect the resolving power?

The size of the slit or aperture has a direct impact on the resolving power. A smaller slit or aperture will produce a greater amount of diffraction, resulting in a decrease in resolving power. This is because smaller openings cause more interference among the light waves, making it more difficult to distinguish between closely spaced objects.

3. Can the wavelength of light affect resolving power through diffraction?

Yes, the wavelength of light can also impact resolving power through diffraction. Longer wavelengths, such as red light, diffract more than shorter wavelengths, such as blue light. This means that for the same size aperture, red light will have a lower resolving power compared to blue light. Therefore, the choice of light wavelength is an important consideration in achieving optimal resolving power.

4. How can the effects of diffraction on resolving power be minimized?

To minimize the effects of diffraction on resolving power, a larger aperture or slit can be used. This allows for less diffraction and interference among the light waves, resulting in better resolution. Additionally, using a light source with a shorter wavelength can also help to minimize the impact of diffraction on resolving power.

5. Are there any other factors besides diffraction that can affect resolving power?

Yes, there are other factors that can affect resolving power, such as the quality of the optical system and the presence of aberrations. These factors can impact the sharpness and clarity of the image, making it more difficult to distinguish between closely spaced objects. Proper calibration and maintenance of the optical system can help to minimize these effects and improve resolving power.

Similar threads

Resolving Power and minimum seperation
    • Introductory Physics Homework Help
Replies
5
Views
4K
What is the Width of the Car Based on Diffraction Limit Problem?
    • Introductory Physics Homework Help
Replies
6
Views
2K
Fraunhofer Diffraction Pattern Ratio of Power Densities
    • Introductory Physics Homework Help
Replies
34
Views
2K
Diffraction grating problem
    • Introductory Physics Homework Help
Replies
10
Views
2K
Diffraction Grating Question, Dispersion and Resolving
    • Introductory Physics Homework Help
Replies
2
Views
4K
Diffraction grating problem involving Snell's Law
    • Introductory Physics Homework Help
Replies
3
Views
5K
The Rayleigh Criterion and the Wavelength of Light
    • Introductory Physics Homework Help
Replies
2
Views
4K
What Is the Smallest Spot Diameter the Human Eye Can Detect?
    • Introductory Physics Homework Help
Replies
4
Views
4K
Calculating Light Spot Size on the Moon for a Diffraction-Limited Laser Beam
    • Introductory Physics Homework Help
Replies
7
Views
1K
Rayleigh criterion (two wavelengths) + diffraction grating
    • Introductory Physics Homework Help
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top