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
Larry drops a 5kg ball off of a building. The ball hits the ground 4.7s later. How tall is the building?
musickatia [10]

Explanation:

Given:

v₀ = 0 m/s

a = 9.8 m/s²

t = 4.7 s

Find: Δy

Δy = v₀ t + ½ at²

Δy = (0 m/s) (4.7 s) + ½ (9.8 m/s²) (4.7 s)²

Δy ≈ 110 m

8 0
3 years ago
A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by υ⃗ =[5.00m/
Reptile [31]
It would possibly be [7.00m/s(0.5613m/s)
8 0
3 years ago
What change does this cause concerning weather?
Vika [28.1K]

Answer:

More extreme weather.

Explanation:

The Conveyor Belt of tides functions on a local and global level to spread out the cold and hot temperature differences on the planet. It is a delicate but important process that is easily disrupted, which causes it to slow down. And when it slows down, all those temperature differences will become more concentrated, causing colder places to be colder and hotter places to be hotter, ultimately leading to more extreme weather events as these cold and hot spots collide more violently than before.

Here's a picture I found on it:

6 0
3 years ago
Read 2 more answers
How would you calculate the spring constant of an unknown spring?
kupik [55]
<span> the </span>spring constant<span> k is the slope of the straight line W versus x plot.</span>
6 0
3 years ago
Do physical changes include changes in the states of matter?
VikaD [51]
I think so yeah if I’m not right sorry
8 0
3 years ago
Read 2 more answers
Other questions:
  • The energy an object acquires when it is exposed to a force is called _____ energy
    5·1 answer
  • An Athlete is injured on field his teammates see that the injury is moderately swollen in the athlete reports the area is numb w
    7·1 answer
  • A positive point charge q1 = +5.00 × 10−4C is held at a fixed position. A small object with mass 4.00×10−3kg and charge q2 = −3.
    6·1 answer
  • The electric field strength E is measured as:
    11·1 answer
  • Charge q is 1 unit of distance away from the source charge S. Charge p is two times further away. The force exerted between S an
    8·2 answers
  • A shuttle changed velocity from 5.0 km/s to 11.9 km/s in 0.5 seconds. What is the acceleration of
    12·1 answer
  • a turtle swimming in a straight line toward shore has a speed of 0.50 m/s after 4.0s its speed is 0.80 m/s what is the turtle's
    6·1 answer
  • Calculate the average (mean) of these numbers: 6, 5, 7, 9.8*
    15·1 answer
  • Joel uses a force of 50 Newtons to hold two weights 0.60 meters above his head. How much work is Joel doing on the weights?
    12·1 answer
  • (a) A long, straight solenoid has N turns, uniform cross-sectional area A, and length l. Show that the inductance of this soleno
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!