the expression for diffraction grating allows to find the results for the questions for the angular separation are:
i) The third order is Δθ = 0.203 rad.
ii) The first order with water is Δθ = 0.046 rad.
The diffraction grating is a system formed by a large number of equally spaced lines whose diffraction is given by the expression.
d sin θ = m λ
Where d is the distance between two lines, θ is the angle of diffraction, the order of diffraction and λ is the wavelength.
i) Let's start by looking for the separation between two lines
Let's use a rule of direct proportions. If there are 300 lines in 1 mm, what distance is there between two lines.
d = 1 lines (1 mm / 300 lines) = 3,333 10⁻³ mm
d = 3.333 10⁻⁶ m
Let's find the angle of diffraction for the third order (m = 3) for each wavelength.
λ₁ = 400 nm = 400 10⁻⁹ m
sin θ₁ = [tex]\frac{m \ \lambda }{d}[/tex]m λ/ d
sin θ₁ = [tex]\frac{3 \ 400 \ 10^{-9} }{3.333 \ 10^{-6} }[/tex]
θ₁ = sin⁻¹ 0.3600
θ₁ = 0.368 rad
λ₂ = 600 nm = 600 10⁻⁹ m
sin θ₂ = [tex]\frac{3 \ 600 \ 10^{-9} }{3.333 \ 10^{-6} }[/tex]
θ₂ = sin⁻¹ 0.5401
θ₂ = 0.571 rad
The angular separation is
Δθ = θ₂ - θ₁
Δθ = 0.571 - 0.368
Δθ = 0.203 rad
ii) In this case, the separation between the network and the observation screen is filled with water.
When the rays leave the network they undergo a refraction process, for which they must comply with the relationship.
[tex]n_i \ sin \theta_1 = n_r \ sin \theta_r[/tex]
The incident side is in the air, therefore its refractive index is n_i = 1 and when it passes into the water with refractive index n_r = 1.33.
Let's start looking for the incident angles for the first order of diffraction.
m = 1
λ₁ = 400 nm
θ₁ = sin⁻¹ [tex]\frac{1 \ 400 \ 10^{-9}}{3.33 \ 10^{-6}}[/tex]
θ₁ = 0.120 rad
λ₂ = 600 nm
θ₂ = sin⁻¹¹ [tex]\frac{1 \ 600 \ 10^{-9} }{3.33 \ 10^{-6}}[/tex]
θ₂ = 0.181 rad
we use the equation of refraction.
[tex]\theta_r[/tex] = sin⁻¹ ([tex]\frac{n_i}{n_r} \ sin \ \theta_i[/tex] )
λ₁ = 400 nm
θ₁ = sin¹ ([tex]\frac{1 sin 0.120}{1.33}[/tex]
θ₁ = 0.090 rad
λ₂ = 600 nm
θ₂ =sin⁻¹ [tex]\frac{1 sin 0.181}{1.33}[/tex]
θ₂ = 0.1358 rad
The angular separation is
Δθ = 0.1358 - 0.090
Δθ = 0.046 rad.
In conclusion using the relation for the diffraction grating we can find the results for the questions about angular separation are:
i) The third order is Δθ = 0.203 rad.
ii) The first order with water is Δθ = 0.046 rad.
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An object of mass 1.0 kg is at rest on a smooth inclined plane with height h, length 8 m,
and which makes an angle of 30° with the horizontal. The object is allowed to move, it
slides down and onto a rough horizontal surface. After traveling a distance of 4 m it hits a spring and travels 1.3 m more, all along the rough horizontal surface. The spring
constant is 26.5 N/m. What is the coefficient of kinetic friction for the horizontal surface?
The coefficient of kinetic friction for the rough horizontal surface is 0.66.
The given parameters;
mass of the object, m = 1 kglength of the inclined plane, L = 8 mangle of inclination of the plane, θ = 30⁰ distance traveled before hitting the spring, d₁ = 4 mdistance traveled after hitting the spring, d₂ = 1.3 mthe spring constant, k = 26.5 N/mApply work-energy theorem; the work done the force of friction is equal to the energy stored in the spring.
[tex]F_kd_1 = \frac{1}{2} kd_2^2\\\\\mu_kmg cos(\theta)d_1 = \frac{1}{2} kd_2^2\\\\\mu_k(1 \times 9.8 \times cos(30)\times 4) = \frac{1}{2} \times 26.5 \times (1.3)^2\\\\33.95\mu_k = 22.39\\\\\mu_k = \frac{22.39}{33.95} \\\\\mu_k = 0.66[/tex]
Thus, the coefficient of kinetic friction for the rough horizontal surface is 0.66.
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the electrical energy used to pump the water up to a mountain lake is 1.2 x 10 to the power 12 J only 6.2 x 10 to the power 11 J of electrical energy is generated when the water is released calculate the efficiency of this energy storage scheme
Answer:
Explanation:
ake is 1.2 x 10^12 J. Only 6.2 x 10^11 J of electrical energy is generated when the water is released. Calculate the efficiency of this energy
When adding vectors, what cannot change?
A. the vectors' length and direction
B. anything can change
C. only the vectors' length
D. only the vectors' direction
please help!!
Answer:
A
Explanation:
you cannot change the length and direction
number A is right I think
Jasmine pushing her little brother on the swing the swing passes back-and-forth 14 times in 40 seconds what is the frequency of the motion and what is superior to the swing
Answer:
Explanation:
frequency f = 14 cycles/40 s
f = 0.35 cycles/s or
f = 0.35 Hz.
I suspect you are more concerned with the PERIOD of the swing rather than what is superior to it. (How would one even compare?)
T = 1/f = 1/0.35
T = 2.85714285...
T = 2.86 s
What element is chemically similar to carbon
nonmental
that should be the answer
Why potential energy is remian constant when solid body is heated?
A rock falls to the ground with a force of 300N and air resistance pushes back up on the rock with a
force of 45N. Which is true of the rock?
Answer:
what are the choices
Explanation:
don't worry i'll edit it
Which of the following statements about migration is true?
a. Migration is always from one region to another.
b. Animals always migrate within a region.
c. Migration always negatively impacts an ecosystem.
d. Animals migrate for various reasons.
Answer:
A and D
b and C are false
Answer:
D. Animals migrate for various reasons.
Explanation:
Got it right on Edge 2023. : )
A__________ shows how velocity changes over time
A Wheatstone Bridge type circuit is shown (10marks) R1=20ohms, R2=10ohms, R3=8ohms, R4=5ohms, and R5=2ohms and also has 10V battery. Determine A. the p.d. between terminals B and D, and (5 marks) B. The value to which R4 must be adjusted in order to reduce the current through R3 to zero (balance the bridge). (5marks)
Answer:
Dunno
Explanation:
Dunno
A brick is thrown upward from the top of a building at an angle of 25 degrees to the horizontal with an initial speed of 15 m/s. If the brick is in flight for 4 s before it hits the ground, how tall is the building?
Answer:
First, find the maximum height, which according to the values given, can be stated as:
H=(u²sin²theta)/2g
u=15m/s, theta=25 degrees, g=9.8m/s²
H= (15² * (sin 25)²))/2*9.8
H= (225*0.179)/19.6
H= 40.275/19.6
=2.06m
To find the velocity at maximum height:
Use the formula
v²=u²-2gH
It's minus because the brick was thrown upwards
So plugging everything into the above formula:
v²=15²-2*9.8*2.06
v²=225–40.376
v²=184.624
v=√184.624
v=13.59m/s
identify impacts of air pollution
Answer:
Explanation:
High levels of air pollution can cause an increased risk of heart attack, wheezing, coughing, and breathing problems, and irritation of the eyes, nose, and throat. Air pollution can also cause worsening of existing heart problems, asthma, and other lung complications.
Ambient air pollution accounts for an estimated 4.2 million deaths per year due to stroke, heart disease, lung cancer and chronic respiratory diseases. Around 91% of the world's population lives in places where air quality levels exceed WHO limits.
Serious Effects of Pollution on Our Humans and Environment
Environment Degradation. The environment is the first casualty for the increase in pollution weather in air or water. ...
Human Health. ...
Global Warming. ...
Ozone Layer Depletion. ...
Infertile Land.
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When the pushing force is increased to 88.2 N, the box just begins to move. What is the Friction Force if it is moving at a constant velocity? What is the coefficient of friction between the ground and box?
In order to calculate frictional force look below..
The formula given by
[tex]\\ \sf\longmapsto F_f=\mu N[/tex]
Or
[tex]\\ \sf\longmapsto F_f=\mu mg[/tex]
u is coefficient of friction
N is normal reaction.
what is deviation of light by prism
Answer:
When a ray of light passes from one medium to another it changes its path, this phenomenon of light is called the deviation of light. When a ray of light passes through a prism it suffers refraction twice. Once while it enters the prism and again while it emerges from it.
From what material did the moon form?How are eras and periods of the geologic time scale named?
Answer:
this
Explanation:
because of this its this ok
Answer: They are named for the places where geologists first described rocks or fossils from that time.
Explanation: ingenuity
Mr. Jones's prescription calls for 1.04 tablets per day. Based on this information, how many tablets should Mr. Jones take per day? a) 1.25 O b) 1.5 c) 1 O d) 2
Due to the fact that no one can consume .04 of a tablet, we can round down this answer to 1. This means that Mr. Jones should take C- 1 tablet per day.
I hope I've helped! :)
Mr. Jones's prescription calls for 1.04 tablets per day. Based on this information, he should take 1 tablet per day. The correct option is C.
What is prescription?The doctor suggests the medicine to be taken by the patient for the treatment of any disease or symptom is called as prescription.
Mr. Jones's prescription calls for 1.04 tablets per day. Based on this information, Mr. Jones must take 1 tablet per day.
No one can consume .04 of a tablet, we can round off 1.04 to 1. This means that Mr. Jones should take 1 tablet per day.
Thus, the correct option is C.
Learn more about prescription.
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cách đổi ev sang kj/mol
If a rock is thrown vertically upward from the surface of Mars with velocity of 20 m/s, its height (in meters) after t seconds is h = 20t − 1.86t2. (a) What is the velocity (in m/s) of the rock after 2 s? 12.56 Correct: Your answer is correct. m/s (b) What is the velocity (in m/s) of the rock when its height is 25 m on its way up? On its way down? (Round your answers to two decimal places.) up 8.07 Incorrect: Your answer is incorrect. m/s down -8.07 Incorrect: Your answer is incorrect. m/s
The velocity of the rock after 2s is 12.56 m/s.
The velocity of the rock at 25 m upwards is 14.68 m/s.
The velocity of the rock at 25 m downwards is -15.97 m/s.
The given parameters;
velocity of the rock, u = 20 m/sheight of the rock, h = 20t - 1.8t²The velocity of the rock after 2s is calculated as follows;
[tex]v = \frac{dh}{dt}= 20 -2(1.86)t \\\\v = 20 - 3.72t\\\\at \ t= 2 \ s \\\\v = 20 - 3.72(2) = 12.56 \ m/s[/tex]
The velocity of the rock when the height is 25 m:
h = 20t - 1.8t²
25 = 20t - 1.8t²
1.8t² - 20t + 25 = 0
solve for the time of motion "t" using quadratic formula
a = 1.8, b = -20, c = 25
[tex]t = \frac{-b \ \ +/- \ \ \sqrt{b^2 - 4ac} }{2a} \\\\t = \frac{-(-20) \ \ +/- \ \ \sqrt{(-20)^2 - 4(1.8\times 25)} }{2(1.8)}\\\\t = 9.67s, \ \ or \ 1.43 \ s[/tex]
The value of t that will give 25 m upwards using the motion model is 1.43 s;
h = 20(1.43) - 1.86(1.43)² = 25 m
The velocity of the rock at 25 m upwards (t = 1.43 s) is calculated as follows;
[tex]v = \frac{dh}{dt} = 20 -3.72t\\\\v = 20 - 3.72(1.43) \\\\v = 14.68 \ m/s[/tex]
The velocity of the rock at 25 m downwards (t = 9.67 s) is calculated as;
[tex]v = \frac{dh}{dt} = 20 - 3.72t\\\\v = 20 - 3.72(9.67)\\\\v = -15.97 \ m/s[/tex]
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In a vacuum light travels at which speed?
Answer:
Light traveling through a vacuum moves at exactly 299,792,458 meters (983,571,056 feet) per second. That's about 186,282 miles per second
Explanation:
(a) Define the term ginning? (b) Name the simple device used for spinning?
A simple device used for spinning is a hand spindle also known as takli.
hope it helps
Ex 2) A cannon ball is shot straight up into the air with an initial velocity of 25 m/s[Up).
What is the maximum height of the cannonball?
Explanation:
The final velocity at the cannon ball's maximum height is zero ([tex]v_y = 0[/tex]). We can use the equation
[tex]v_y^2 = 0 = v_{0y}^2 - 2gy_{max}[/tex]
[tex]\Rightarrow y_{max} = \dfrac{v_{0y}^2}{2g}[/tex]
[tex]y_{max} = \dfrac{(25\:\text{m/s})^2}{2(9.8\:\text{m/s}^2)}[/tex]
[tex]\:\:\:\:\:\:\:=31.9\:\text{m}[/tex]
What provides the centripetal force for the moon's orbit around Earth?
Answer:
Gravitational attraction provides the centripetal force needed to keep planets in orbit around the Sun and all types of satellite in orbit around the Earth. This centripetal force is supplied by gravity. The Earth's gravity keeps the Moon orbiting us. Centripetal force is perpendicular to velocity and causes uniform circular motion. The gravitational attraction of the Sun is an inward force acting on Earth. This force produces the centripetal acceleration of the orbital motion. Centripetal forces are always directed toward the center of the circular path.
Explanation:
Answer: C.
the gravitational pull of the Sun
Explanation: plato :3
Hope this helps!
Ex 3) A tennis player lobs the tennis ball up in the air during a serve at a rate 3 m/s.
How long will it take the tennis ball to reach its maximum height?
Two horses are side by side on a carousel. Which has a greater tangential speed the one closer to the center or the one farther from the center? Explain your answer.
Answer:
The horse father from the center has a greater tangential speed. Although both horses complete one circle in the same time period, the one farther from the center covers a greater distance during that same period.
Explanation:
9. Steradian is the angel which lies in:
a) One dimension
b) Two dimensions
Answer:
B
Explanation:
B
10 basic rules of badminton?
Explanation:
Rules
A match consists of the best of three games of 21 points.
The player/pair winning a rally adds a point to its score.
At 20-all, the player/pair which first gains a 2-point lead wins that game.
At 29-all, the side scoring the 30th point wins that game.
The player/pair winning a game serves first in the next game.
A badminton match can be played by two opposing players (singles) or four opposing players (doubles).
A competitive match must be played indoors utilising the official court dimensions.
A point is scored when the shuttlecock lands inside the opponent's court or if a returned shuttlecock hits the net or lands outside of the court the player will lose the point.
At the start of the rally, the server and receiver stand in diagonally opposite service courts.
A legal serve must be hit diagonally over the net and across the court.
A badminton serve must be hit underarm and below the server's waist height with the racquet shaft pointing downwards, the shuttlecock is not allowed to bounce. After a point is won, the players will move to the opposite serving stations for the next point.
The rules do not allow second serves.
During a point a player can return the shuttlecock from inside and outside of the court.
A player is not able to touch the net with any part of their body or racket.
A player must not deliberately distract their opponent.
A player is not able to hit the shuttlecock twice.
A 'let' may be called by the referee if an unforeseen or accidental issue arises.
A game must include two rest periods. These are a 90-second rest after the first game and a 5-minute rest after the second game.
Question 2 of 10
You are riding a bicycle. If you apply a forward force of 125 N, and you and
the bicycle have a combined mass of 82 kg, what will be the forward
acceleration of the bicycle? (Assume there is no friction.)
A. 1.67 m/s2
B. 3.37 m/s2
C. 0.66 m/s2
D. 1.52 m/s2
O
Answer:
D - 1.52 m/s2
Explanation:
force: 125 N
Mass: 82 kg
you just divide the force by the mass which would be approximately 1.52
The gravitational force between two objects is 2700 N. What will be the gravitational force between the objects if the distance between them triples?
F = GMm/r^2
So F is proportional to 1/r^2
F2 = 2700 x ( 1 / 3^2 ) = 300N
A stimulus that increses the occurance of a response is called
Answer:
reinforcing stimulus
Explanation:
Think its correct
Answer:
reinforcing stimulus
Explanation:
because it increases the occurence of a response