Two lasers are shining on a double slit, with slit separation d. Laser 1 has a wavelength of d/20, whereas laser 2 has a wavelength of d/15. The lasers produce separate interference patterns on a screen a distance 6.00 m away from the slits. Which laser has its first maximum closer to the central maximum?
What is the distance Image for Two lasers are shining on a double slit, with slit separation d. Laser 1 has a wavelength of d/20, whereas las between the first maxima (on the same side of the central maximum) of the two patterns?
Two lasers are shining on a double slit, with slit separation d. Laser 1 has a wavelength of d/20, whereas las= m
What is the distance Deltay_max-min between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum?
Deltay_max-min = m

A)   Therefore laser1 has the maximum closest to the central maximum

B) Δₓ = 0.8

Explanation:

A) The expression for the constructive interference of a double slit is

           d sin θ  = m λ

let's use trigonometry to find the angle

          tan θ = y / L

in interference phenomena the angles are small

         tan θ = sin θ / cos θ = sin θ

         sin θ = y / L

we subjugate

         d y / L = m λ

         y = m λ L / d

let's apply this equation for each case

a) Lares 1 has a wavelength λ₁ = d / 20, the screen is at L = 6.00 m

they ask us for the first axiom m = 1,

let's calculate

           y₁ = 1 (d / 20) 6.00 / d

           y₁ = 0.3

Laser 2, λ₂ = d / 15

            λ₂ = 1 (d / 15) 6.00 / d

           λ₂ = 0.4

Therefore laser1 has the maximum closest to the central maximum

b) let's find the distance of each requested value

second maximum m = 2 of laser 1

            yi '= 2 (d / 20) 6 / d

            y1 '= 0.6

3rd minimum of laser 2

the expression for destructive interference is

               d sinθ = (m + 1/2) lam

               y = (m ) λ L / d

in this case m = 3

let's calculate

              y2 '= (3+0.5) (d / 15) 6 / d

              y2 '=21/15

They ask us for the dalt of these interference

            Δₓ = y3 -y2'          

           Δₓ = 21/15 - 0.6

           Δₓ = 0.8

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

-it's clean and sustainable

-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

-almost everywhere, the shallow ground or upper 10 feet of the earth's surface maintains a nearly constant temperature between 50° and 60°f (10° and 16°c)

-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

-in the winter, the heat pump removes heat from the heat exchanger and pumps it into the indoor air delivery system

-in the summer, the process is reversed, and the heat pump moves heat from the indoor air into the heat exchanger

-the heat removed from the indoor air during the summer can also be used to provide a free source of hot water