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
Karolina [17]
3 years ago
14

There are 5510 lines per centimeter in a grating that is used with light whose wavelegth is 467 nm. A flat observation screen is

located 1.03 m from the grating. What is the minimum width that the screen must have so the centers of all the principal maxima formed on either side of the central maximum fall on the screen
Physics
1 answer:
Mademuasel [1]3 years ago
4 0

Answer:

1.696 nm

Explanation:

For a diffraction grating, dsinθ = mλ where d = number of lines per metre of grating = 5510 lines per cm = 551000 lines per metre and λ = wavelength of light = 467 nm = 467 × 10⁻⁹ m. For a principal maximum, m = 1. So,

dsinθ = mλ = (1)λ = λ

dsinθ = λ

sinθ = λ/d.

Also tanθ = w/D where w = distance of center of screen to principal maximum and D = distance of grating to screen = 1.03 m

From trig ratios 1 + cot²θ = cosec²θ

1 + (1/tan²θ) = 1/(sin²θ)

substituting the values of sinθ and tanθ we have

1 + (D/w)² = (d/λ)²

(D/w)² = (d/λ)² - 1

(w/D)² = 1/[(d/λ)² - 1]

(w/D) = 1/√[(d/λ)² - 1]

w = D/√[(d/λ)² - 1] = 1.03 m/√[(551000/467 × 10⁻⁹ )² - 1] = 1.03 m/√[(1179.87 × 10⁹ )² - 1] = 1.03 m/1179.87 × 10⁹  = 0.000848 × 10⁻⁹ = 0.848 × 10⁻¹² m = 0.848 nm.

w is also the distance from the center to the other principal maximum on the other side.

So for both principal maxima to be on the screen, its minimum width must be 2w = 2 × 0.848 nm = 1.696 nm

So, the minimum width of the screen must be 1.696 nm

You might be interested in
A particle with charge Q and mass M has instantaneous speed uy when it is at a position where the electric potential is V. At a
olga nikolaevna [1]

Answer:

A

Explanation:

Ke = 1/2 MV^2

4 0
2 years ago
Pls help in these 2 questions
Nadya [2.5K]

Answer:

Taking forces along the plane

F cos θ - M g sin θ -100 = M a       net of forces along the plane

F = (M a + M g * .5 + 100) / .866     solving for F

F = (80 * 1.5 + 80 * 9.8 * .5 + 100) / .866 = 707 N

F = 707 N acting along the plane

Fn = F sin θ + M g cos θ       forces acting perpendicular to plane

Fn = 707 * 1/2 + 80 * 9.8 * .866 = 1030 Newtons   forces normal to plane

(this would give a coefficient of friction of 100 / 1030 = .097 = Fn)

4 0
2 years ago
By what factor must the amplitude of a sound wave be increased in order to increase the intensity by a factor of 9?a. 9 b. 2 c.
Marta_Voda [28]

Answer:

option D

Explanation:

given,

intensity\ \alpha \ (Amplitude)^2

increase the intensity by factor of 9

    I₁ = I₀

    I₂ = 9 I₀

now,

\dfrac{I_1}{I_2}=\dfrac{A_1^2}{A_2^2}

\dfrac{I_0}{9I_0}=(\dfrac{A_1}{A_2})^2

(\dfrac{A_1}{A_2})^2=\dfrac{1}{9}

\dfrac{A_1}{A_2}=\dfrac{1}{3}

      A₂ = 3 A₁

hence, amplitude increase with the factor of 3

so, the correct answer is option D

4 0
2 years ago
Read 2 more answers
Planets in our solar system do not revolve around the sun in perfect circles. Their orbits are more like ovals that scientists d
galben [10]
Planets in our solar system do not revolve around the sun in perfect circles. Their orbits are more like ovals that scientists describe as elliptical. It is one of Kepler's laws. The sun is the focus of all the planets. The correct answer is D.
7 0
3 years ago
A 7 kg sled is initially at rest on a horizontal road. the sled is pulled a distance of 2.9 m by a force of 42 n applied to the
Artemon [7]
I have no idea on this question.
6 0
3 years ago
Other questions:
  • What is the difference in the charges on a ballon rubbed in your hair and a glass rod rubbed
    5·1 answer
  • Why is object 2 accelerating while object 1 remains stationary?
    10·1 answer
  • An electron moves through a uniform electric field E = (2.00î + 5.40ĵ) V/m and a uniform magnetic field B = 0.400k T. Determine
    6·1 answer
  • A 2.00-kg textbook rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter
    5·1 answer
  • A 5.1-m-diameter merry-go-round is initially turning with a 4.1 s period. It slows down and stops in 25 s . Part A Before slowin
    12·1 answer
  • A rope holding a brick is hanging from the ceiling of an elevator at rest. If the elevator accelerates
    15·1 answer
  • What mathematical formula is needed to determine the student's displacement from point A to C? (Hint: think
    11·1 answer
  • Why do scientists sometimes discuss the possibility of silicon as a basic element for life?
    9·1 answer
  • How can larger telescopes
    13·1 answer
  • The magnitude of the force associated with the gravitational field is constant and has a value f. A particle is launched from po
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!