Question

In: Physics

You stand on a straight desert road at night and observe a vehicle approaching. This vehicle...

You stand on a straight desert road at night and observe a vehicle approaching. This vehicle is equipped with two small headlights that are 0.621m apart. At what distance, in kilometers, are you marginally able to discern that there are two headlights rather than a single light source? Take the wavelength of the light to be 559nm and your pupil diameter to be 4.69mm. Answer in km!

Solutions

Expert Solution

The two point light sources (distant headlights) each form concentric-ring diffraction patterns on the retina due to the circular aperture of the eye pupil .. these two neighbouring patterns overlap on the retina making it difficult to resolve two close individual sources.

According to the Rayleigh criterion the two sources are just resolved when the central maxima of one pattern overlaps the first minima of the other pattern .. in other words the two patterns have the same angular separation as the first minima has from the peak of the central maxima.

For a circular aperture, the first minima (n=1) has an angular separation from the peak of the central maxima given by ..
Sinθ = 1.22 λ / d .. (d = aperture/pupil diameter)
Sinθ = 1.22 x 559×10-9m / 4.69×10-3m ..

Sinθ =1.4541×10-4

For the headlights .. sinθ ≈ (light separation) / (distance from eye)

1.4541×10-4= 0.621m / D
D = 0.621/ 1.4541×10-4

►D = 0.427×104 m = 4.27 km


Related Solutions

You stand near the edge of a swimming pooland observe through the water an object lying...
You stand near the edge of a swimming pooland observe through the water an object lying on the bottom of thepool. Which of the following statements correctly describes whatyou see? Please ChooseThe apparent depth of the object is less than the real depth.The apparent depth of the object is greater than the real depth.There is no difference between the apparent depth and the actual depth of the object.
At starbase Faraway Point, you observe two spacecraft approaching from the same direction. The Picard approaches...
At starbase Faraway Point, you observe two spacecraft approaching from the same direction. The Picard approaches starbase Faraway Point with a speed of 0.806 c, and the La Forge approaches the starbase with a speed of 0.918 c. Suppose the Picard now launches a probe toward the starbase. What velocity must the probe have relative to the Picard if it is to be at rest relative to the La Forge? What velocity must the probe have relative to the Picard...
1. If you are driving 85 km/h along a straight road and you look to the...
1. If you are driving 85 km/h along a straight road and you look to the side for 2.0s, how far do you travel during this inattentive period? Assume that your speed remains constant. 2. A child, who is 46 m from the bank of a river, is being carried helplessly downstream by the river's swift current of 1.5 m/s. As the child passes a lifeguard on the river's bank, the lifeguard starts swimming in a straight line (perpendicular to...
Designed a Flowchart where you have to ask road type and speed of the vehicle from...
Designed a Flowchart where you have to ask road type and speed of the vehicle from user and then decide whether a car is over-speeding, is under-speed or it is moving with the allowed speed. Develop program using C language The allowed speed limit is given in the following table. See the following conditions: Road Type     Speed Limit Local Street 20-30 km/h Main Street   31-40 km/h Main Road    41-90 km/h High way       91-110 km/h Table 2: Normal (Allowed)
A car travels along a straight east-west road. A coordinate system is established on the road,...
A car travels along a straight east-west road. A coordinate system is established on the road, with x increasing to the east. The car ends up 19 mi west of the intersection with Mulberry Road. (A) If its displacement was -21 mi , how far from Mulberry Road did it start?
. A jeep is traveling on a straight road and it leaves a junction at time...
. A jeep is traveling on a straight road and it leaves a junction at time t = 0 second. It is then accelerates at 4 m/s 2 for 4 seconds. Suddenly, when the driver shifting the gears, there is no acceleration of the jeep for 1 second. After that, it is continue to accelerates at 5.5 m/s 2 for 5 seconds and maintain the speed it reached. On the other hand, a car leaves at the same junction as...
On a dark desert highway, a car leaves a gas station and heads straight for 10...
On a dark desert highway, a car leaves a gas station and heads straight for 10 km, heading exactly northeast. (i.e., directed 45 degrees northward of due east). The car then turns onto a dirt road and drives completely straight until it reaches a hotel located exactly 12 km north and 9.0 km east of the gas station. How far did the car drive along the straight dirt road?
a stunt driver's car is moving at 24.2 m/s along a straight road. The road comes...
a stunt driver's car is moving at 24.2 m/s along a straight road. The road comes to an abrupt stop 21.2 m before a drop off. The coefficient of friction of the road is 0.712, and the coefficient of friction of the dirt between the road and the drop off is 0.426. What is the minimum distance at which the driver can behin to apply the brakes and still prevent himselff from going over the edge?
You are driving along straight road. You cover 200 miles in 4 hours? Does that mean...
You are driving along straight road. You cover 200 miles in 4 hours? Does that mean that your speedometer read 50 mph for your entire trip? Is is necessary that your speedometer register 50 mph at least once during the trip? Use math to explain your answer. I understand that your speedometer would not be 50mph for the entire trip, but I am not sure how to explain it using math.
Consider driving a car in one direction along a straight road for 10 minutes. You start...
Consider driving a car in one direction along a straight road for 10 minutes. You start from rest. During the first 1 minute, you speed up with constant acceleration until you reach 60 m/s. During the next 5 minutes, you maintain constant speed at 60 m/s. During the final 4 minutes, you have constant negative acceleration (i.e. deceleration) until you are not moving. How far in total did you travel during the whole 10 minutes? Express your answer in units...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT