1) Yellow light that has a wavelength of 560 nm passes through two narrow slits that are 0.300 mm apart. An interference pattern is produced on a screen 160 cm distant. What is the location of the first-order maximum?
2) A communication satellite is orbiting 36 000 km above Earth’s surface. Two cities, 3500 km apart are transmitting to and receiving signals from each other. Find the time required to transmit a signal from one city to the other. They are equidistant from the satellite.
x(min) =±(2k-1)•λL/2•d,
x(min1) =λL/2•d =560•10^-9•1.6/2•0.3•10^-3 =1.49•10^-3m =1.49 mm
s=2•sqrt{(3.6•10^7)²+(3.5•10^3)²} =7.2•10^4.
t=s/c=7.2•10^4/3•10^8=0.24 s.
I don't understand why you're multiplying by two for the second question.
nevermind I get it
1) To determine the location of the first-order maximum in the interference pattern, we can use the equation for the position of the maximum on the screen.
The equation is given by:
y = (λ * L) / d
Where:
y is the position of the maximum on the screen,
λ is the wavelength of the light,
L is the distance from the slits to the screen, and
d is the spacing between the slits.
In this case, the wavelength of the yellow light is 560 nm, which is 560 x 10^-9 meters. The distance from the slits to the screen is 160 cm, which is 160 x 10^-2 meters. The spacing between the slits is 0.300 mm, which is 0.300 x 10^-3 meters.
Substituting these values into the equation, we have:
y = (560 x 10^-9 * 160 x 10^-2) / (0.300 x 10^-3)
Simplifying the equation, we get:
y = 3.74 m
Therefore, the location of the first-order maximum is 3.74 meters from the central maximum on the screen.
2) To calculate the time required to transmit a signal from one city to the other, we need to consider the distance between the cities and the speed of the signal.
The signal needs to travel from one city to the satellite and then from the satellite to the other city. Since the cities are equidistant from the satellite, we can assume that the distance between each city and the satellite is 18,000 km (half the total distance of 36,000 km).
The total distance the signal has to travel is then 18,000 km + 18,000 km = 36,000 km.
The speed of light in a vacuum is approximately 3 x 10^8 meters per second.
To convert the total distance from kilometers to meters, we multiply 36,000 km by 1000, which gives us 36,000,000 meters.
To calculate the time required to transmit the signal, we divide the distance by the speed of light:
time = distance / speed
time = 36,000,000 meters / (3 x 10^8 meters per second)
Simplifying the equation, we get:
time = 0.12 seconds
Therefore, it would take approximately 0.12 seconds to transmit a signal from one city to the other city when they are equidistant from the satellite.