1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kobusy [5.1K]
3 years ago
13

Parallel rays of monochromatic light with wavelength 582 nm illuminate two identical slits and produce an interference pattern o

n a screen that is 75.0 cm from the slits. The centers of the slits are 0.640 mm apart and the width of each slit is 0.434 mm. If the intensity at the center of the central maximum is 4.40×10^−4 W/m^2.
Required:
What is the intensity at a point on the screen that is 0.710 mm from the center of the central maximum?
Physics
1 answer:
Airida [17]3 years ago
8 0

Answer:

  I = 0.56 10⁻⁴ W / m²

Explanation:

Double-slit interference is described by the expression

         d sin θ = m λ

if we use trigonometry we can find the angle

        tan θ= y / L

how the angles are small

       tan θ = sin θ / cos θ = sin θ

      sin θ = y / L

we substitute

       d y / L = m λ

if we take into account that each slit also produces a diffraction phenomenon, the intensity distribution is the product of the intensity of the slits by the intensity of the diffraction process

      I = I₀ cos² (d a)   [(sin ba) / ba]²

      a = π sin θ /λ

       

where the separation of the slits and b is the width of the slits

we substitute

     I = I₀ [cos (d a)]²  [sin ba  /ba]²

     a = π y / (L λ)

let's reduce the magnitudes to the SI system

     λ = 582 nm = 582 10⁻⁹ m

     L = 75.0 cm = 75.0 10⁻² m

     d = 0.640 mm = 0.640 10⁻³ m

     b = 0.434 mm = 0.434 10⁻³ m

     Io = 4.40 10⁻⁴ W / m²

let's calculate for y = 0.710 mm = 0.710 10⁻³ m

     a = π 0.710 10⁻³ / (75 10⁻² 582 10⁻⁹)

      a = 5.11004 10³

I = 4.40 10⁻⁴ [cos (0.640 10⁻³ 5.11004 10³)]² (sin (0.434 10⁻³ 5.11004 10³) / (0.434 10⁻³ 5.11 10³)²

      I = 4.40 10⁻⁴ cos² (3.2704)   (sin 2.2178 / 2.2178)²

remember that the angles are in radians

 

      I = 4.40 10⁻⁴   0.9835  (0.79789 / 2.2178)²

      I = 4.40 10⁻⁴   0.9835    0.1294

      I = 0.56 10⁻⁴ W / m²

You might be interested in
Why cant soy sauce freeze
juin [17]
The salt content in soy
8 0
3 years ago
Read 2 more answers
Where is potential energy the greatest on a rollercoaster?
lidiya [134]
On a roller coaster, the greatest potential energy is at the highest point of the roller coaster
4 0
3 years ago
The quadriceps muscles pull on the patella simultaneously. Below are the forces from each
Nostrana [21]

Based on the calculation of the resultant of vector forces:

  1. the resultant force due to the quadriceps is 1795 N
  2. the resultant force due to the quadriceps is 1975 N. Training and strengthening the vastus medialis results in a greater force of muscle contraction.

<h3>What is the resultant force due to the quadriceps?</h3>

The resultant of more than two vector forces is given by:

  • F = √Fₓ² + Fₙ²

where:

  • Fₓ is the sum of the horizontal components of the forces
  • Fₙ is the sum of the vertical components of the forces
  • Fx = F₁cosθ + F₂cosθ + F₃cosθ + F₄cosθ
  • Fₙ = F₁sinθ + F₂sinθ + F₃sinθ + F₄sinθ
  • F₁ = 680N, θ = 90 = 30 = 120°
  • F₂ = 220 N, θ = 90 + 16 = 106°
  • F₃ = 600 N, θ = 90 + 15 = 105°
  • F₄ = 480 N, θ = 90 - 35 = 55°

then:

Fx = 680 * cos 120 + 220 * cos 106 + 600 * cos 105 + 480 * cos 55

Fx = -280.6 N

Fₙ = 680 * sin 120 + 220 * sin 106 + 600 * sin 105 + 480 * sin 55

Fₙ = 1773.1 N

then:

F = √(-280.6)² + ( 1773.1)²

F = 1795.16 N

F ≈ 1795 N

Therefore, the resultant force due to the quadriceps is 1795 N

<h3>What would happen if the vastus medialis was trained and strengthened to contract with 720N of force?</h3>

From the new information provided:

  • F₁ = 680N, θ = 90 = 30 = 120°
  • F₂ = 220 N, θ = 90 + 16 = 106°
  • F₃ = 600 N, θ = 90 + 15 = 105°
  • F₄ = 720 N, θ = 90 - 35 = 55°

then:

Fx = 680 * cos 120 + 220 * cos 106 + 600 * cos 105 + 720 * cos 55

Fx = -142.95 N

Fₙ = 680 * sin 120 + 220 * sin 106 + 600 * sin 105 + 720 * sin 55

Fₙ = 1969.72 N

then:

F = √(-142.95)² + ( 1969.72)²

F = 1974.9 N

F ≈ 1975 N

Therefore, the resultant force due to the quadriceps is 1975 N.

Training and strengthening the vastus medialis results in a greater force of muscle contraction.

Learn more about resultant of forces at: brainly.com/question/25239010

3 0
2 years ago
How much heat is released as a 5.89 kg block of aluminum cools from 462 °C to 315 °C. The specific heat capacity of aluminum is
s2008m [1.1K]
Mass, m = 5890g
Change in temperature, θ = Final_temperature - Initial_temperature
= 315 - 462°C
= -147°C

Specific heat capacity of aluminum, c = 0.900 J/(g*K) 
=mcθ
=5890g x 0.900 J/(g*K) x -147°C
=-779,247j

Answer would be C. 
5 0
3 years ago
Read 2 more answers
What tool would you use to separate nails from gravel
Minchanka [31]
It would be a wire mesh
7 0
2 years ago
Read 2 more answers
Other questions:
  • A chain lying on the ground is 11 meters long and its mass is 95 kilograms. The chain is threaded through a pulley, which is fix
    15·1 answer
  • What mathematical formula correctly expresses the relationship between force, mass and acceleration? A. m = F + a B. F = m / a C
    10·1 answer
  • Light propagate faster through medium “a” than medium “b”
    6·1 answer
  • Kecepatan sebuah benda dinyatakan dengan persamaan vx=8t+2 vy=12+2t, jika posisi awal pastikel (2,5), maka posisi benda pada saa
    6·1 answer
  • Give 10 examples of units you might use or see in any given day
    6·1 answer
  • 7. Mac and Tosh are arguing about the track design. Mac claims that the car is moving fastest at point F because it is furthest
    13·1 answer
  • 2.
    12·1 answer
  • The tension of a guitar string is increased by 40%. By what factor odes the fundamental frequency of vibration change? a. 1.13 b
    15·1 answer
  • calculate the work done by 2N force directed at 30 degree to the vertical to move a 500g box a horizontal distance of 400 cm acr
    13·1 answer
  • Go to his profile and roast the mess out of him plzz 403665fl 50 points
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!