1) If the first order maximum of He-Ne light exits a diffraction grating at an angle of 40.7o, at what angle will the first order maximum of violet light with a wavelength of 418 nm exit?
What is He-Ne light?????
2) The most efficient antennae have a size of half the wavelength of the radiation they are emitting. How long should an antenna be to broadcast at 980 kHz?
He-Ne light is a gas laser in which He is excited, and those ions then collide with Neon to release energy. Of the most common spectrums of this laser, 633 nm is the most common wavelength.
d sinTheta=m lambda
d = 633*E-9/sin40.7
so, the question: d sinGamma=m lambda
633E-9/sin40.7 * sinGamma=418E-9
solve for The angle Gamma.
b. 980khz*wavelenth= speed light
solve fodr wavelength, then the size of the antenna is half that.
HeNe laser operates at a wavelength of 632.8 nm in the red part of the visible spectrum
d•sinφ = k•λ,
for He-Ne:
d•sin40.7º =1•632.8•10^-9….(1)
For violet light:
d•sinφ=1•418•10^-9 ……(2)
Divide(1) by (2)
d•sin40.7º/ d•sin φ =632.8•10^-9/418•10^-9,
sinφ = sin40.7º •418/632.8 = 0.433.
φ =arcsin 0.433 =25.68º.
λ = c/f = 3•10^8/980000 =305.9 m
L = λ/2 =153 m.
1) He-Ne light refers to the red laser light produced by a helium-neon gas laser. It has a wavelength of about 632.8 nm.
To find the angle at which the first order maximum of violet light with a wavelength of 418 nm will exit the diffraction grating, we can use the formula for calculating the angle of diffraction:
sin(θ) = mλ/d
where θ is the angle of diffraction, m is the order of the maximum, λ is the wavelength of the light, and d is the spacing between the grating lines.
Let's assume that the spacing between the grating lines (d) remains constant for both He-Ne light and violet light.
For He-Ne light:
sin(θ) = λ/632.8 nm
sin(θ) = λ/6.328 x 10^-4 μm
For violet light:
We can substitute the values into the equation:
sin(θ) = λ/(6.328 x 10^-4 μm)
sin(θ) = 418 nm / (6.328 x 10^-4 μm)
sin(θ) ≈ 0.6614
To find the angle θ, we can use the inverse sine (sin^-1) function:
θ = sin^-1(0.6614)
θ ≈ 41.1°
Therefore, the first order maximum of violet light with a wavelength of 418 nm will exit the diffraction grating at an angle of approximately 41.1°.
2) To determine the length of an antenna needed to broadcast at a specific frequency, we can use the formula:
Length of antenna = λ/2
where λ is the wavelength of the radiation.
Given that the broadcasting frequency is 980 kHz, we need to convert it to wavelength units (meters) using the speed of light:
c = λ * f
where c is the speed of light (approximately 3 x 10^8 m/s), λ is the wavelength, and f is the frequency.
Rearranging the equation, we have:
λ = c/f
Substituting the values:
λ = (3 x 10^8 m/s) / (980,000 Hz)
λ ≈ 306.12 m
Now we can calculate the length of the antenna:
Length of antenna = λ/2
Length of antenna = 306.12 m / 2
Length of antenna ≈ 153.06 m
Therefore, to broadcast at 980 kHz, the antenna should have a length of approximately 153.06 meters.
1) He-Ne light refers to the light emitted by a helium-neon laser. In order to determine the angle at which the first order maximum of violet light will exit a diffraction grating, we can use the equation for the grating equation:
sinθ = mλ/d
Where:
- θ is the angle at which the maximum is observed
- m is the order of the maximum (first order in this case)
- λ is the wavelength of the light
- d is the spacing between the lines on the diffraction grating
Let's find the spacing between the lines on the diffraction grating. For a diffraction grating, the spacing is usually given in terms of the number of lines per unit length, called the groove density (G). The formula to convert groove density to spacing (d) is:
d = 1/G
Now let's substitute the given values into the grating equation for both He-Ne light and violet light.
For He-Ne light:
- m = 1 (first order)
- λ = unknown
- d = unknown
- θ = 40.7°
To solve for the wavelength (λ) and spacing (d), we would need additional information such as the groove density of the grating or the number of lines on the grating.
2) The length of an antenna can be calculated using the formula:
Antenna length = (speed of light) / (2 * frequency)
Let's substitute the given value into the formula to calculate the antenna length required to broadcast at a frequency of 980 kHz.
- Frequency = 980 kHz = 980,000 Hz
- Speed of light = 3 x 10^8 meters/second
Antenna length = (3 x 10^8) / (2 * 980,000)
Now calculate the value using the formula to find the antenna length.