What is the Width of the Car Based on Diffraction Limit Problem?

In summary, the problem involves a child standing at the edge of a highway watching her grandparents' car drive away at a constant speed. After 8.3 minutes, the car's two taillights appear to merge into one. Using the equations Θ = 1.22 λ/D and distance = time x speed, the width of the car can be calculated. However, the location of the child in relation to the two taillights affects the calculation, as standing behind one light would mean the other light is only 1.87m away.
  • #1
grantaere
15
0

Homework Statement


A child is standing at the edge of a straight highway watching her grandparents' car driving away at a constant 22.4 m/s. The air is perfectly clear and steady, and after 8.3 minutes the car's two taillights (654 nm) appear to merge into one. Assuming the diameter of the child's pupils is 4.76 mm, calculate the width of the car.

Homework Equations


Θ = 1.22 λ/D

The Attempt at a Solution


I solved for theta by plugging in the wavelength and diameter (came out to be 1.676 e -4 rad), then found the distance from the car using distance = time x speed = 11155.2m and multiplied that by the angle to find what I thought would be half the width of the car, and multiplied that by two to get an answer of 3.74m-- however, that's apparently incorrect and I'm not sure what I did wrong. Any help with be really appreciated. Thank you!
 
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  • #2
grantaere said:
... by the angle to find what I thought would be half the width ...

"Half?"
 
  • #3
Bystander said:
"Half?"

Wouldn't the distance to the car be a line that forms a right triangle?
 
  • #4
Which tail-light of Grandmother's car is Little Red Riding Hood standing behind?
 
  • #5
Bystander said:
Which tail-light of Grandmother's car is Little Red Riding Hood standing behind?

I assumed she's between the two, since it doesn't specify... would where she is change the answer??
 
  • #6
If she's standing behind one, how much further away could the other be?
 
  • #7
Bystander said:
If she's standing behind one, how much further away could the other be?

Ahh, I see now- so I don't need to multiply by two because if she stands behind one light, the other is only 1.87m away. Thank you so much!
 

1. What is the diffraction limit problem?

The diffraction limit problem is a phenomenon in optics where the resolution of an imaging system is limited by the wave nature of light. This means that even with a perfect lens, there is a limit to how small of an object can be resolved. This is due to the diffraction of light waves as they pass through the lens, causing blurring and reducing the sharpness of the image.

2. How does the diffraction limit affect imaging systems?

The diffraction limit affects imaging systems by limiting the smallest details that can be resolved in an image. This can be a problem for microscopy, astronomy, and other fields where high resolution is necessary. It also means that increasing the magnification of a lens will not necessarily improve the resolution, as it will still be limited by diffraction.

3. Can the diffraction limit problem be overcome?

While the diffraction limit problem cannot be completely overcome, there are ways to improve resolution in imaging systems. Techniques such as deconvolution, using shorter wavelengths of light, and using adaptive optics can help to reduce the effects of diffraction and improve resolution.

4. What is the relationship between aperture size and diffraction limit?

The size of the aperture, or opening, in an imaging system plays a significant role in the diffraction limit problem. A larger aperture allows more light to pass through, which can improve the resolution. However, as the aperture gets larger, the diffraction effects also become more pronounced, limiting the resolution.

5. How does the diffraction limit problem impact scientific research?

The diffraction limit problem has a significant impact on scientific research, particularly in fields that rely on high-resolution imaging. It can limit the ability to observe and study small structures and details, which can hinder progress in understanding and advancing various fields of science. To overcome this, scientists often use advanced imaging techniques and software to improve resolution and overcome the diffraction limit problem.

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