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

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SUMMARY

The discussion focuses on calculating the width of a car based on the diffraction limit problem, specifically using the formula Θ = 1.22 λ/D. The child observes the car's taillights merging at a distance of 11155.2 meters after 8.3 minutes of travel at 22.4 m/s. The initial calculation yielded an incorrect width of 3.74 meters due to a misunderstanding of the geometry involved. The correct approach clarifies that the width should not be multiplied by two if the observer is positioned behind one taillight, resulting in a final width of 1.87 meters.

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grantaere
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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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grantaere said:
... by the angle to find what I thought would be half the width ...

"Half?"
 
Bystander said:
"Half?"

Wouldn't the distance to the car be a line that forms a right triangle?
 
Which tail-light of Grandmother's car is Little Red Riding Hood standing behind?
 
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??
 
If she's standing behind one, how much further away could the other be?
 
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!
 

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