You need to focus a 10 mW, 632.8 nm Gaussian laser beam that is 5.0 mm in diameter into a sample. You have access to a lens with a focal length of 6.0 cm and focal length of 12.0 cm. For both lenses, the light fills the size of the lens. Using the Gaussian beam equations, what is the smallest diameter of the beam (known as the beam waist) for each lens

Answers

Answer 1

Answer:

ee that the lens with the shortest focal length has a smaller object

           

Explanation:

For this exercise we use the constructor equation or Gaussian equation

        [tex]\frac{1}{f} = \frac{1}{p} + \frac{1}{q}[/tex]

where f is the focal length, p and q are the distance to the object and the image respectively.

Magnification a lens system is

          m = [tex]\frac{h'}{h}[/tex] = - [tex]\frac{q}{p}[/tex]

             h ’= -\frac{h q}{p}

In the exercise give the value of the height of the object h = 0.50cm and the position of the object p =∞

Let's calculate the distance to the image for each lens

f = 6.0 cm

           [tex]\frac{1}{q} = \frac{1}{f } - \frac{1}{p}[/tex]

as they indicate that the light fills the entire lens, this indicates that the object is at infinity, remember that the light of the laser rays is almost parallel, therefore p = inf

          q = f = 6.0 cm

for the lens of f = 12.0 cm q = 12.0 cn

to find the size of the image we use

           h ’= h q / p

where p has a high value and is the same for all systems

           h ’= h / p q

Thus

f = 6 cm h ’= fo 6 cm

 

f = 12 cm h ’= fo 12  cm

therefore we see that the lens with the shortest focal length has a smaller object


Related Questions

PLEASE PLEASE PLEASE HELP

Answers

Answer:

just use y = mx + b to create an equation of the line in the graph.

then you can plug in 15 for x and then convert 1.5 hours into minutes and plug it in as well.

you dont even need to make an equation for a line. just add 0.2 for every 3 mins.

at 9, it's 0.6, so at 12 it would be 0.8, and then 15 it would be 1.0.

go again all way for 1. 5 hours.

Explanation:

the slope is 0.1/1.5 so you equation would be y = 0.1/1.5x

the slope is rise/run.

Modify how could you charge the electric circuit shown below to allow lightbulb a to stay lit even if lightbulb b is removed from its base?

Answers

When a circuit is complete, or closed, electrons can flow from one end of a battery all the way around, through the wires, to the other end of the battery. Along its way, it will carry electrons to electrical objects that are connected to it – like the light bulb – and make them work!

A traffic light consists of a horizontal member attached to a vertical support post. The horizontal member extends 7 m to the left of the support post and has a constant mass density of 15 kg/m. Each traffic light has mass of 10 kg, and the street sign has a mass of 4.5 kg. Make sure the connection between the horizontal member and the vertical support post is strong enough to withstand the forces exerted on the horizontal member. Calculate the effects of the forces resulting from the two traffic lights and the street sign on the horizontal member.

Answers

Answer:

τ = 539 N m

Explanation:

Let's use the rotational equilibrium relationship, where we set our reference system at the junction of the poles and the counterclockwise rotations we consider positive

               τ = Σ τ_i

the mass of the traffic lights is m₁ = 10 kg, the mass of the sign m₂ = 4.5kg and suppose the worst case all the elements connected at the end (x = 7 m)

               τ = 2 m₁  x + m₂ x + m₃ x / 2

we calculate the mass of the horizontal pole using the concept of linear density

               λ = m₃ / l

               m₃ = λ l

we substitute

                τ = (2m₁ + m₂) x + λ l x / 2

                τ = x (2m₁ + m₂ +λ l / 2)

                 

let's calculate

               τ = 7 (2 10 + 4.5 + 15 7/2)

               τ = 539 N m

therefore, this is the torque that the joint between the two posts must resist

When an object falls, its:
A. PE increases and KE decreases.
B. PE does not change.
C. PE and KE both increase.
D. PE decreases and kE increases​

Answers

Answer:

Option D. is correct.

Explanation:

The object's mechanical energy refers to the sum of the potential and kinetic energies of the object. When an object falls, its potential energy (PE) decreases, and its kinetic energy (KE) increases. The increase in kinetic energy is exactly equal to the decrease in potential energy.

Option D. is correct.

A 80 N force is needed to slide a 50.0 kg box across a flat surface at a constant velocity. What is the coefficient of kinetic friction between the box and the floor

Answers

Answer:

0.16

Explanation:

Given data

Force F= 80N

Mass m= 50kg

Reaction R= Weight= mg= 50*9.81= 490.5N

We know that

F=UR

Substitute and solve of U

U=F/R

U= 80/490.5

U=0.16

Hence the coefficient of friction is 0.16

During a phase change the temperature of a substance remains constant this is because during a phase heat changes the ____ energy of particles in a substance without changing their ____ energy

Answers

Answer:

Explanation:

individual and then net

hope that helps I could be wrong about this one though

4. Taylor Swift pushes Kanye West,
headfirst fearless, off a high dive with and
initial speed of 6m/s. If the platform is 20m
high, what is Kanye's impact velocity with
the water? (velocity and angle)

Answers

The velocity would be 3.33333

Explanation: to find velocity you divide distance with time! (Hope this helps)

You drive on Interstate 10 from San Antonio to Houston, half the time at 75 km/h and the other half at 106 km/h. On the way back you travel half the distance at 75 km/h and the other half at 106 km/h. What is your average speed (a) from San Antonio to Houston, (b) from Houston back to San Antonio, and (c) for the entire trip

Answers

Answer:

Explanation:

a ) from San Antonio to Houston let distance be d km .

Average speed = total distance / total time

time = distance / speed

Total time = (d / 2 x 75 ) +( d / 2 x 106 )

= .0067 d + .0047 d

= .0114 d

Average speed  = d / .0114 d = 87.72 km /h

b ) from Houston back to San Antonio

Total time = (d / 2 x 106 ) +( d / 2 x 75 )

= .0047 d + .0067 d

= .0114 d

Average speed  = d / .0114 d = 87.72 km /h

c )

For entire trip :

total distance = 2d

total time = 2 x .0114 d

Average speed  = 2 d / 2 x .0114 d

= 87.72 km /h .

Which type of wall would make the best soundproofing for room?
A.
1.0 centimeter thick glass
OB.
two layers of 0.5 centimeter thick glass with 0.5 centimeters of air between them
C.
two layers of 0.5 centimeter thick glass with 0.3 centimeters of vacuum between them
OD.
1.0 centimeter thick steel

Answers

Among the options given, the choice that would make the best soundproofing for a room is option C: two layers of 0.5 centimeter thick glass with 0.3 centimeters of vacuum between them.

Soundproofing is achieved by reducing the transmission of sound waves from one side of the wall to the other. In this case, the combination of two layers of glass with a vacuum between them helps to reduce sound transmission effectively.

Glass is a denser material compared to air or vacuum, so it naturally provides some sound insulation. Adding an extra layer of glass creates a barrier that helps to further dampen sound vibrations. The vacuum between the glass layers acts as an additional sound barrier, as sound waves have difficulty propagating through a vacuum due to the absence of a medium for transmission.

On the other hand, a single layer of 1.0 centimeter thick glass (option A) or two layers of 0.5 centimeter thick glass with 0.5 centimeters of air between them (option B) would provide some sound reduction but not as effective as the combination of glass layers with a vacuum in option C.

1.0 centimeter thick steel (option D) would have high density and mass, which could help with sound insulation to some extent. However, steel can still transmit vibrations and might not be as effective as the combination of glass layers with a vacuum in option C for soundproofing a room.

For more such questions on Soundproofing

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Two stationary positive point charges, charge 1 of magnitude 3.95 nC and charge 2 of magnitude 1.80 nC, are separated by a distance of 39.0 cm. An electron is released from rest at the point midway between the two charges, and it moves along the line connecting the two charges.What is the speed of the electron when it is 10.0 cm from charge 1?

Answers

Answer:

the speed of the electron from charge q1 is 7.17×10⁶ m/s

Explanation:

Given the data in the question;

the potential at the center of the two charges will be;

V = k( q1/(d/2) + q2/(d/2)

so we substitute

V = (9×10⁹)( (3.95×10⁻⁹/(0.39/2) + 1.80×10⁻⁹/(0.39/2)

V = 265.4 V

the potential at a distance of 10 cm from the charges will be

V = k( q1/(d1) + q2/(d2)

(d1 = 10cm = 0.1m and d2 = 39cm - 10cm = 29cm = 0.29m )

V' = (9×10⁹)( (3.95×10⁻⁹/0.1 + 1.80×10⁻⁹/0.29

V' = 411.4 V

Now, from the conservation of energy the speed of the electron from charge q1 will be;

E = ( V' - V) qe

1/2mv² = ( V' - V) qe

v² = [( V' - V) qe] / 1/2m

v =√ ([( V' - V) qe] / 1/2m)

v =√ ([2( V' - V) qe] / m)

we substitute

v =√ (2[( 411.4  - 265.4) 1.6×10⁻¹⁹] / 9.1×10³¹)

v = 7.17×10⁶ m/s

Therefore, the speed of the electron from charge q1 is 7.17×10⁶ m/s

An upward force of 32.6 N is applied via a string to lift a ball with a mass of 2.8 kg. (a) What is the gravitational force acting on the ball? (b) What is the net force acting upon the ball? (c) What is the acceleration of the ball?

Answers

Answer:

a) Fg = -27.4 N

b) Fnet = 5.2 N

c) a = 1.9 m/s2

Explanation:

a)

There are two forces acting on the ball, one directed upward (assuming this direction as positive, along the y-axis) which is the tension on the string (lifting force), and another aimed downward, which is the attractive force due to gravity.Applying the Newton's Universal Law of Gravitation to a mass close to the surface of the Earth (in this case the ball), we can take the acceleration due to gravity like a constant, that we call by convention g, equal to -9.8 m/s2.So, we can write the following expression for Fg:

       [tex]F_{g} = m*g = 2.8 kg*(-9.8m/s2) = -27.4 N (1)[/tex]

b)

The net force on the ball, will be just the difference between the lifting force (32.6 N) and the force due to gravity, Fg:

       [tex]F_{net} = T -F_{g} = 32.6 N - 27.4 N = 5.2 N (2)[/tex]

c)

According Newton's 2nd Law, the acceleration caused by a net force on a point mass (we can take the ball as one) is given by the following expression:

       [tex]a = \frac{F_{net} }{m} = \frac{5.2N}{2.8kg} = 1.9 m/s2 (3)[/tex]

A hovercraft is being driven across a lake on a very windy day. The wind exerts a force of 5000 N north on the hovercraft. The propellers driving the hovercraft also exert a force.


What is the net force (to 3.s.f ) on the hovercraft when the force applied to the hovercraft by the propellers is: 10 000 N west

Answers

Answer:

The net force on the hovercraft is 11200 N.

Explanation:

Given;

force exerted on the hovercraft by wind, F₁ = 5000 N north

force exerted on the hovercraft by the propeller, F₂ = 10,000 N west

The net force on the hovercraft is calculated as;

[tex]F_{net} = \sqrt{F_1^2 + F_2^2} \\\\F_{net} = \sqrt{5000^2 + 10,000^2} \\\\F_{net} = 11180.34 \ N\\\\F_{net} = 11200 \ N \ (3.s.f)[/tex]

Therefore, the net force on the hovercraft is 11200 N.

models are frequently used in science to assist in the understanding of complex information. Models can include items like a working volcano, and aquarium, or a stream table. What type of model are each of these items?

A) two dimensional
b) three dimensional
c) mental explanation
d) Computer simulation

Answers

B. Three dimensional I’m almost positive

Does light travel faster in seawater or in fresh water? Does light travel faster in seawater or in fresh water? Light travels faster in seawater, because the index of refraction is smaller in seawater. Light travels faster in fresh water, because the index of refraction is smaller in fresh water. Light travels faster in fresh water, because the index of refraction is larger in fresh water. Light travels faster in seawater, because the index of refraction is larger in seawater.

Answers

No

because that is a light

The light travel faster in fresh water as compare to sea water.

When light goes from denser to rare medium the speed of light is increases.When light travel from rare to denser medium the speed of light is decreases.The reflective index of denser medium is more as compare to rare medium.The reflective index of sea water is more as compare to fresh water.

Hence, the light travel faster in fresh water as compare to sea water.

Learn more:

https://brainly.com/question/10769980

Physical science-current can be increased by...

Answers

i think it’s d
sry if not

Option 3.) Increasing the voltage across the wire.

I know that the other answers are incorrect because, for one thing, the more resistance in a substance, the less flow of the current there is. Also, using a longer wire doesn't change anything, it just makes a electrical current go on longer. Lastly decreasing the voltage would make the current decrease in the atoms that flow through it to power an object.

-R3TR0 Z3R0

A 45.0-kg girl stands on a 13.0-kg wagon holding two 18.0-kg weights. She throws the weights horizontally off the back of the wagon at a speed of 6.5 m/s relative to herself . Assuming that the wagon was at rest initially, what is the speed of the girl relative to the ground after she throws both weights at the same time

Answers

Answer:

v = 4.0 m/s

Explanation:

Assuming no external forces acting during the instant that the girl throws the weights, total momentum must be conserved.Since all the masses at rest initially, the initial momentum must be zero.So, due to momentum must keep constant, final momentum must be zero too, as follows:

       [tex]p_{f} = m_{w} * v_{w} + m_{g+w} *v_{g+w} = 0 (1)[/tex]

Assuming the direction towards the back of the wagon as positive, and replacing the masses in (1), we can solve for vg, as follows:

       [tex]v_{g+w} =- \frac{m_{w} *v_{w}}{m_{g+w} } = - \frac{36.0kg *6.5m/s}{58.0kg } = -4.0m/s (2)[/tex]

This means that the girl (along with the wagon on she is standing) will move at a speed of 4.0 m/s in an opposite direction to the one she threw the weights.


Marlon is studying a crab population. He has a large batch of crabs that were captured in the ocean. He places a plastic tag on a leg of each crab and releases the entire batch back into the ocean. The tags
include a phone number that can be called it the crabs are caught. For each crab, Marion records the location he released the crab and the location that it was recaptured. What can Marion measure with
this data
А
the speed the crabs traveled
B
the velocity the crabs traveled
the acceleration of the crabs
D
the displacement of the crabs

Answers

First time I did it I got 2143658709

An ideal monatomic gas initially has a temperature of 300 K and a pressure of 5.79 atm. It is to expand from volume 420 cm3 to volume 1450 cm3. If the expansion is isothermal, what are (a) the final pressure and (b) the work done by the gas

Answers

Answer:

a) The final pressure is 1.68 atm.

b) The work done by the gas is 305.3 J.

Explanation:

a) The final pressure of an isothermal expansion is given by:

[tex] T = \frac{PV}{nR} [/tex]

[tex] T_{i} = T_{f} [/tex]

[tex] \frac{P_{i}V_{i}}{nR} = \frac{P_{f}V_{f}}{nR} [/tex]

Where:

[tex]P_{i}[/tex]: is the initial pressure = 5.79 atm

[tex]P_{f}[/tex]: is the final pressure =?

[tex]V_{i}[/tex]: is the initial volume = 420 cm³

[tex]V_{f}[/tex]: is the final volume = 1450 cm³

n: is the number of moles of the gas

R: is the gas constant

[tex] P_{f} = \frac{P_{i}V_{i}}{V_{f}} = \frac{5.79 atm*420 cm^{3}}{1450 cm^{3}} = 1.68 atm [/tex]

Hence, the final pressure is 1.68 atm.

b) The work done by the isothermal expansion is:

[tex] W = P_{i}V_{i}ln(\frac{V_{f}}{V_{i}}) = 5.79 atm*\frac{101325 Pa}{1 atm}*420 cm^{3}*\frac{1 m^{3}}{(100 cm)^{3}}ln(\frac{1450 cm^{3}}{420 cm^{3}}) = 305.3 J [/tex]

Therefore, the work done by the gas is 305.3 J.

I hope it helps you!        

The spectrum of a star shows a set of dark absorption lines equivalent to the absorption lines of the Sun but with one exception: Every line appears at a slightly longer wavelength, shifted toward the red end of the spectrum. What conclusion can be drawn from this observation

Answers

Answer:

The shift in the emission spectra of the relative velocity between the star and our planet, is called the relativistic doppler effect

Explanation:

The absorption and emission spectra are measured differently, the emission spectrum is the spectrum emitted by the star and the absorption spectrum is the absorption of these lines by the gases of our atmosphere, this absorption occurs for relatively broad Δλ.

The shift in the emission spectra of the relative velocity between the star and our planet, is called the relativistic doppler effect and has a red shift if the star moves away from us.

           [tex]f_o = f_s \sqrt{\frac{1- v/c}{1 + v/c} }[/tex]

___is found in fruits and honey. *
1.Maltose
2.Sucrose
3.Fructose
4.Galactose

Answers

Answer:

3. Fructose

Explanation:

Fructose is a sugar found naturally in fruits, fruit juices, some vegetables and honey.

it is number 3 (Fructose)

A 20.0 N force is necessary to stretch a spring 0.500 m. What is the spring constant of this spring?

Answers

The spring constant : k = 40 N/m

Further explanation

Given

Force = 20 N

The displacement of the spring=x=0.5 m

Required

The spring constant = k

Solution

Hooke's Law

F = k.x

k = F/x

Input the value :

k = 20/0.5

k = 40 N/m

Two people are playing tug-of-war. Due to their choice of footwear, theircoefficient of static friction is different. Participant 1 has a mass of 60 kg, acoefficient of static friction of 2.0, and can pull with a maximum force of1000 N. Participant 2 has a mass of 80 kg and a coefficient of staticfriction of 1.2, and can pull with a maximum force of 1200 N. Who wins?

Answers

Answer:

Participant 1 wins

Explanation:

Coefficient of static, μ = F/N, where F is the frictional force and N is the normal force.

The force exerted by each participant is the sum of the frictional force acting on each of them and the maximum force with which each participant pulls on the rope.

Frictional force, F =  μ * N

Normal force, N = mass * acceleration due to gravity, g

For Participant 1; μ = 2.0, mass = 60 kg, g = 9.8 m/s²

Frictional force = 2.0 * 60 * 9.8 = 1176 N

Total force = (1176 + 1000) = 2176 N

For Participant 2; μ = 1.2, mass = 80 kg, g = 9.8 m/s²

Frictional force = 1.2 * 80 * 9.8 = 940.8N

Total force = (940.8 + 1200) N = 2140.8 N

From the values obtained above, Participant 1 exerts more force than Participant 2, therefore, Participant 1 wins

What type of change happens when the powder inside a firework is burned?

A.Freezing occurs from a chemical change.
B.Light is produced by a chemical change.
C.Rotting occurs from a chemical change.
D.Rust is produced by a chemical change.

Answers

Answer:

B light is produced by chemical change

Explanation:

im not the smartest but if you think about it, fireworks make bright lights. And what do they have: powders.

(but I still could wrong, sorry if I am)

B- because fireworks produce heat light and loud sounds all caused by chemicals. The only right choice would be B

Take 47 points. Hurry Someone save me just look the picture ​

Answers

Answer:

suppose buying pizza for a work party leads to positive morale and to the work being done in half the time. Pizza is the independent variable, Work speed is the dependent variable, The mediator, the middle man without which there would be no connection, is positive morale. Denaturation, in biology, the process of modifying the molecular structure of a protein. Denaturation involves the breaking of many of the weak linkages, or bonds (e.g., hydrogen bonds), within a protein molecule that is responsible for the highly ordered structure of the protein in its natural (native) state.

Explanation:

hope this helps have a good rest of your day :) ❤

Explanation:

HW1. For example, suppose buying pizza for a work party leads to positive morale and to the work being done in half the time. Pizza is the independent variable, Work speed is the dependent variable, The mediator, the middle man without which there would be no connection, is positive morale.

HW2. The word denature means to render food unpleasant or dangerous to consume, it is denatured by adding a substance known as a denaturant. Aversive agents—primarily bitterants and pungent agents—are used to produce an unpleasant flavor.

Hope It Helps U

Please Mark As Brainl

5. (Liquids Gases) have particles with enough energy to spread out
throughoutcontainer. *
A)Liquids
B)Gases

Answers

Answer:

b gases

Explanation:

this is because gases spread out through out the entire container because they have no definite shape and are always moving.

Gases is the correct answer :))

Which two options are homogeneous mixtures?
A. Sand
B. A wet sponge
C. Liquid dishwashing soap
O D. Vinegar

Answers

Answer:

Liquid dishwashing soap

Vinegar

Explain why objects in water appear to be a different size then the same objects above the water.

Answers

Answer:

the answer is the third one since water reflects it

Explanation:

The other name of eureka can

Answers

Answer:

I found it!

Explanation:

Answer:

Explanation:

displacement vessels

The can is filled to the top with water and the object placed in it. The volume of the object is equal to the volume of the water that is forced through the spout. Eureka cans are named after a scientist called Archimedes who first recorded this idea. They are sometimes also called displacement vessels.

A student drove to the university from her home and noted that the odometer reading of her car increased by 17.9 km. The trip took 26.6 min.
a) What was her average speed, in kilometers per hour?
b) IS she returned home by the same path 7 h 30 min after she left, what was her average speed and velocity for the entire trip?

Answers

Answer:

See calculation below

Explanation:

Average speed = Distance/Time

a) Given

Distance = 17.9km

Time = 26.6minutes

Time = 26.6/60 hr

Time = 0.443hr

Average speed  = 17.9/0.443

Average speed = 40.38km/hr

b) If she returned home by the same path 7 h 30 min after she left, the distance will be the same;

Distance = 17.9km

Time = 7.5hr

Average speed = 17.9/7.5

Average speed = 2.387km/hr

Velocity of the entire trip = 40.38km/hr + 2.387km/hr

Velocity of the entire trip = 42.77km/hr

Hence the velocity of the entire trip is 42.77km/hr

Which of the following statements are true?
a. By convention, the direction of a current is taken to be the direction of flow for negative charges.
b. When an electric field is applied to a conductor, the free electrons move only in the direction opposite the applied electric field.
c. Current is the total amount of charge that passes through a conductor's full cross section at any point per unit of time.
d. In order to maintain a steady flow of current in a conductor, a steady force must be maintained on the mobile charges.
e. In a circuit, current is delivered by the positive terminal of a battery, and it is used up by the time it returns to the negative terminal of the battery.

Answers

Answer:

A, C, D and E are the true statement about current flowing.

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