A diffraction grating, ruled with 300 lines per mm, is illuminated with a white light source at normal incidence.
(i) What is the angular separation, in the third-order spectrum, between the 400 nm and 600 nm lines? [5]
(ii) Water (of refractive index 1.33) now fills the whole space between the grating and the screen. What is the angular separation, in the first-order spectrum, between the 400 nm and 600 nm lines? [5]​

Answers

Answer 1

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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Related Questions

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?

Answers

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/m

Apply 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​

Answers

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!!

Answers

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

Answers

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

Answers

nonmental

that should be the answer

Why potential energy is remian constant when solid body is heated?

Answers

the temperature remains constant because the given heat is used to increase only the potential energy of the molecules of the given substance (which results in the change of its state) and not the kinetic energy as temperature of a body is actually the measure of the average kinetic energy of its molecules.

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?

Answers

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.

Answers

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

Answers

Velocity time graph goes into the blank hope it helps please mark me brainliest

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)​

Answers

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?

Answers

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

Answers

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.

Please allow me to know if I helped you by clicking thank you, rating or brainly.

Thank you,

Miss Hawaii

Long-term health effects from air pollution include heart disease, lung cancer, and respiratory diseases such as emphysema. Air pollution can also cause long-term damage to people's nerves, brain, kidneys, liver, and other organs. Some scientists suspect air pollutants cause birth defects. Air pollution can damage crops and trees in a variety of ways. Ground-level ozone can lead to reductions in agricultural crop and commercial forest yields, reduced growth and survivability of tree seedlings, and increased plant susceptibility to disease, pests and other environmental stresses. Exposure to high levels of air pollution can cause a variety of adverse health outcomes. It increases the risk of respiratory infections, heart disease and lung cancer. Both short and long term exposure to air pollutants have been associated with health impacts. More severe impacts affect people who are already ill.


Hope it can help you:)

I DO NOT WANT LINKES OR …………..

Answers

B-
Reasoning: a vacuum is empty space, therefore light can travel through, sound waves cannot travel through empty space!

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?​

Answers

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​

Answers

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?

Answers

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

Answers

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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#SPJ2

cách đổi ev sang kj/mol

Answers

Để chuyển đổi phép đo electronvolt thành phép đo kilojoule, hãy nhân năng lượng với tỷ lệ chuyển đổi. Năng lượng tính bằng kilojoules bằng electronvolt nhân với 1,6022E-22.

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

Answers

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 - 1.8t²

The 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?

Answers

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?​

Answers

(a) Define the term ginning?

Ginning is the process of removing the seeds and debris from cotton. The term comes from the cotton gin, invented by Eli Whitney in 1794.

(b) Name the simple device used for spinning?

hand spindle

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?

Answers

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?​

Answers

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?

Answers

10 seconds is the time it will take to reach 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.​

Answers

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

Answers

Answer:

B

Explanation:

B

10 basic rules of badminton?​

Answers

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

Answers

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?

Answers

F = GMm/r^2

So F is proportional to 1/r^2

F2 = 2700 x ( 1 / 3^2 ) = 300N

As two objects are separated from each other, the force of gravitational attraction between them also decreases. ... If the separation distance between any two objects is tripled (increased by a factor of 3), then the force of gravitational attraction is decreased by a factor of 9 (3 raised to the second power).

A stimulus that increses the occurance of a response is called

Answers

Answer:

reinforcing stimulus

Explanation:

Think its correct

Answer:

reinforcing stimulus

Explanation:

because it increases the occurence of a response

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