A ray of white light strikes the surface of a 4.0-cm-thick slab of flint glass as shown in the figure. As the ray enters the glass, it is dispersed into its constituent colors. Estimate how far apart (in mm) the rays of deepest red and deepest violet light are as they exit the bottom surface.

Answers

Answer 1

Answer: The separation distance between the rays of deepest red and deepest violet light is approximately 0.1 mm.

Explanation: To solve this problem, we need to use the formula for the deviation angle of light passing through a prism:

θ = (n − 1) α

where θ is the deviation angle, n is the refractive index of the material, and α is the prism angle.

For a thin slab of glass, we can approximate the deviation angle as:

θ ≈ (n − 1) t α / λ

where t is the thickness of the slab and λ is the wavelength of the light.

For red light, λ ≈ 700 nm, and for violet light, λ ≈ 400 nm. The refractive index of flint glass is typically around 1.6.

The prism angle can be found from the geometry of the figure:

sin(α) = 2 cm / (2 cm + 4 cm) ≈ 0.333

so α ≈ 19.5°

Substituting all these values into the formula, we get:

θ_red ≈ (1.6 − 1) × 4.0 cm × 19.5° / (700 nm) ≈ 0.138°

θ_violet ≈ (1.6 − 1) × 4.0 cm × 19.5° / (400 nm) ≈ 0.242°

The separation angle between the two colors is the difference between these angles:

θ_sep = θ_violet − θ_red ≈ 0.104°

To find the separation distance on the screen, we need to multiply this angle by the distance from the slab to the screen:

d = 2 cm + 4 cm ≈ 6 cm

Using the small-angle approximation, we can write:

d_sep ≈ d θ_sep

Plugging in the values, we get:

d_sep ≈ 6 cm × 0.104° ≈ 0.010 cm ≈ 0.1 mm

So the separation distance between the rays of deepest red and deepest violet light is approximately 0.1 mm.

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Related Questions

A wind turbine has a total input power of 2 500 kW.
The efficiency of the wind turbine is 20%.
What is the useful output power of the turbine?

Answers

Answer:

Output power = 500 KW

Explanation:

Given the following data;

Efficiency = 20%

Input power = 2500 KW

To find the output power;

\( Efficiency = \frac {Out-put \; power}{In-put \; power} * 100 \)

Substituting into the equation, we have;

LET Output power = OP

\( 20 = \frac {OP}{2500} * 100 \)

Cross-multiplying, we have;

\( 20 * 2500 = OP * 100 \)

\( 50000 = OP * 100 \)

\( OP = \frac {50000}{100} \)

Output power = 500 KW

A capacitor is discharged through a 20.0 Ω resistor. The discharge current decreases to 22.0% of its initial value in 1.50 ms.
What is the time constant (in ms) of the RC circuit?
a) 0.33 ms
b) 0.67 ms
c) 1.50 ms
d) 3.75 ms

Answers

The time constant (in ms) of the RC circuit is 3.75 ms. Hence, the correct option is  (d) 3.75 ms.


The rate of decay of the current in a charging capacitor is proportional to the current in the circuit at that time. Therefore, it takes longer for a larger current to decay than for a smaller current to decay in a charging capacitor.A capacitor is discharged through a 20.0 Ω resistor.

The discharge current decreases to 22.0% of its initial value in 1.50 ms. We can obtain the time constant of the RC circuit using the following formula:$$I=I_{o} e^{-t / \tau}$$Where, I = instantaneous current Io = initial current t = time constant R = resistance of the circuit C = capacitance of the circuit

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The time constant of the RC circuit is approximately 0.674 m s.

To determine the time constant (τ) of an RC circuit, we can use the formula:

τ = RC

Given that the discharge current decreases to 22.0% of its initial value in 1.50 m s, we can calculate the time constant as follows:

The percentage of the initial current remaining after time t is given by the equation:

I(t) =\(I_oe^{(-t/\tau)\)

Where:

I(t) = current at time t

I₀ = initial current

e = Euler's number (approximately 2.71828)

t = time

τ = time constant

We are given that the discharge current decreases to 22.0% of its initial value. Therefore, we can set up the following equation:

0.22 =\(e^{(-1.50/\tau)\)

To solve for τ, we can take the natural logarithm (ln) of both sides:

ln(0.22) = \(\frac{-1.50}{\tau}\)

Rearranging the equation to solve for τ:

τ = \(\frac{-1.50 }{ ln(0.22)}\)

Calculating this expression:

τ ≈ 0.674 m s

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Is it possible to have acceleration at constant velocity

Answers

Answer:

No

Explanation:

It is not possible to have acceleration at constant velocity

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No it is not possible it would be possible to have a negative acceleration tho

what mass of oxygen gas (o2) should occupy a 25.0 l container when the pressure is 665 torr and the temperature is 55.0ºc?

Answers

The mass of oxygen gas (O2) occupying the 25.0 L container at a pressure of 665 torrs and a temperature of 55.0ºC is approximately 28.288 grams.

To determine the mass of oxygen gas (O2) occupying a 25.0 L container, we can use the ideal gas law equation:

PV = nRT

Where:

P is the pressure of the gas (in atm)

V is the volume of the gas (in liters)

n is the number of moles of gas

R is the ideal gas constant (0.0821 L·atm/(mol·K))

T is the temperature of the gas (in Kelvin)

First, we need to convert the given temperature from Celsius to Kelvin:

T(K) = T(°C) + 273.15

T(K) = 55.0°C + 273.15

T(K) = 328.15 K

Next, we need to convert the given pressure from torr to atm:

P(atm) = P(torr) / 760

P(atm) = 665 torr / 760

P(atm) ≈ 0.875 atm

Now, we can rearrange the ideal gas law equation to solve for the number of moles (n):

n = PV / RT

n = (0.875 atm) * (25.0 L) / [(0.0821 L·atm/(mol·K)) * (328.15 K)]

n ≈ 0.884 mol

Finally, to calculate the mass of oxygen gas (O2), we need to use the molar mass of oxygen, which is 32.00 g/mol (16.00 g/mol for each oxygen atom):

Mass = n * molar mass

Mass = 0.884 mol * 32.00 g/mol

Mass ≈ 28.288 g

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what energy does a car have when you fill it up

Answers

Answer:

mechanical energy

Explanation:

Answer:

When you fill it up its chemical energy but it gets transformed into mechanical energy.

Explanation:

The internal combustion engine, which is utilized in most automobiles, has allowed for the transfer of chemical energy into mechanical energy. This provides locomotion for the vehicle as it is driving.

A homeowner is thinking about replacing his filament bulbs with LED bulbs.

A 12 W LED bulb gives the same light output as a 60 W filament bulb.

Suggest reasons why the homeowner is likely to choose LED bulbs.

Use the information given in the table

Answers

Answer:

because it would reduce the use of more electricity for same light output

Because it takes less energy and the light output is the same

A crane uses an average force of 5,200 N to left a girder 25m. How much work does the crane do on the girder?

Answers

Answer:

130,000 J

Explanation:

The work done by an object can be found by using the formula

workdone = force × distance

From the question we have

workdone = 5200 × 25

We have the final answer as

130,000 J

Hope this helps you

A coin is dropped off of a building from rest at a height of 155 meters. What is the velocity of the coin as it hits the ground?

Answers

Answer:

period let the coin do what it do

Explanation:

On a road trip, you travel from the 100 mile marker to the 250 mile marker in 2 hours. How fast are you going?

Answers

2.5 miles an hour but yea hope that helps

If you build a common source amplifier with NMOS input transistor and we want a current source as a load and that current source goes from VDD to a node so what would be the type of the current source?

Answers

If you build a common-source amplifier with an NMOS input transistor, and you want a current source as a load, and that current source goes from VDD to a node, the type of current source would be the diode-connected transistor.

An NMOS current source implemented as a diode-connected transistor is a type of bipolar transistor circuit that creates a constant current from an input voltage. The collector and emitter of the bipolar transistor are connected together in the circuit, effectively turning the transistor into a diode. The main advantage of diode-connected transistors is that they can generate currents of a specific magnitude and not be influenced by changes in the supply voltage.

The current generated by the diode-connected transistor is almost completely determined by the physical characteristics of the transistor and the biasing resistors used in the circuit. Another advantage of diode-connected transistors is that they may be cascaded in series to create current sources of various sizes. These devices have been commonly used to generate reference currents, voltage-to-current (V-I) converters, and bias currents in linear integrated circuits. So therefore diode-connected transistor is the type of current source, if you build a common-source amplifier with an NMOS input transistor, and you want a current source as a load, and that current source goes from VDD to a node.

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For a series circuit, as lights are added, the voltage across each bulb increases/ decreases/ remains the same ?

For a series circuit, as lights are added, the current across each bulb increases/ decreases/ or remains the same ?


Answers

For a series circuit, as lights are added, the current across each bulb decreases.  

A magnifier allows one to look at a very near object by forming an image of it farther away. The object appears larger. To create a magnifier, one would use a.

Answers

In order to create a magnifier in convex lens, you should choose a short focal length that is lesser than 1 meter.

What is a convex lens?

A convex lens is also referred to as converging lens and it can be defined as a type of lens that typically causes parallel rays of light with respect to its principal axis to come to a focus (converge) and form a real image.

In Science, a magnifier refer to an optical instrument that allow us to look at a very near object because its image is generally formed farther away. Thus, the image of the object appears to be much larger.

In this context, you should choose a short focal length that is lesser than 1 meter when you want to create a magnifier in convex lens because the nearer the object is to the lens, the larger would be the image formed.

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A brick sliding across a smooth floor has a coefficient of static friction of s=0.23 and a coefficient of kinetic friction of k=0.15. If the brick has a mass of 0.85 kg, how much friction will the brick experience as it slides?

Answers

Answer:

0.029325

Explanation:

0.23x0.15=0.0345

0.0345x0.85=0.029325

Answer:

1.25 N

Explanation:

It will experience friction from the kinetic friction component because it is moving ...there will be no component of static friction.

Ff = F n x  k

   =   (.85)(9.81)  x (.15) = 1.25 N

Physics grade 7. Free fall!!!!

Physics grade 7. Free fall!!!!

Answers

Answer:

Hello this is allina from brainly. I'll be helping you today. Use the formula, v=gt to find the velocity.

For example, the velocity after one second would be g * t = 10 m/s^2 * 1, which would be 10 m/s.

So, just put the time into the equation:

ii. 20 m/s

iii. 30 m/s

iv. 50 m/s

The formula d = 1/2gt^2 is for finding the distance it has fallen in free fall.

SO plug in the value for t into the equation.

i. 5 m

ii. 20 m

iii. 45 m/s

iv. 125 m/s

Use the previous formula (v = gt) to find the time it has fallen:

v = gt

30 m/s = 10 m/s^2 * t

t = 3 s

So it has fallen for 3 seconds.

Use the 3 seconds to find the distance it has fallen in free fall:

d = 1/2gt^2

d = 1/2 * 10 m/s^2 * 3^2 s

d = 45 m

Explanation:

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que cantidad de calor absorbe una masa de hielo de 200kg que esta a 0°C para fundirse totalmente?

Answers

Answer:

m - 200 kg

ti - 0⁰c

clF - 79,7kcal, kg ( calor latente de fusión)

pf - 0⁰c

formulas:

QL- cL.m

solución - Ap camosla ecqación.

QL- (79,7 kcal,kg) .200 kg

Resultado ,la cantidad de calor absorbe lamasa de hieloes

Q2 -15,940 kcal

what is the acceleration caused by gravity on earth

Answers

Answer:

Explanation:

It's 9.8 m/s^2

as a car drives past a person standing on a sidewalk, the driver keeps a hand on the horn. how does the pitch of the horn differ for the driver and the person standing on the sidewalk?

Answers

Answer:

While the car is going towards the standing person on the sidewalk he is listening the pitch of the horn higher then it is.

When the car passes the person on the sidewalk and goes away, the horn's pitch become lower (for the person standing on the sidewalk).

For the driver, the pitch is always the same.

Explanation:

Is the doppler effect.

When the car is approaching, the sound waves must travel a smaller space than the previous one and they take less time to reach the standing person. So, sound waves reach the standing person with a higher frequency.

It happens the opposite when the car is going away: the sound waves need to travel more space and take more time to reach the person on the sidewalk. So, the frequency of the waves is lower.

What is the density of a substance that has a mass of 10 grams and volume of 15cm3

Answers

1.5 gram per cubic centimeter

x-ray tubes currently used by dentists often have accelerating voltages of 80 kv. what is the minimum wavelength of the x rays they produce?

Answers

The minimum wavelength of x-rays produced by the x-ray tubes currently used by dentists can be calculated using the equation λ_min = hc / eV, where λ_min is the minimum wavelength, h is Planck's constant, c is the speed of light, e is the charge of an electron, and V is the accelerating voltage. Plugging in the values, we get λ_min = (6.626 x 10^-34 J s x 3 x 10^8 m/s) / (1.602 x 10^-19 C x 80 kV) = 0.025 nanometers (or 25 angstroms). Therefore, the x-rays produced by these x-ray tubes have a minimum wavelength of 0.025 nm.

Wavelength is commonly designated by the Greek letter lambda (λ). The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.

Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space or along a wire. In wireless systems, this length is usually specified in meters (m), centimeters (cm) or millimeters (mm).

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an object is dropped from the top of a building which is 75 meters high. what's it's velocity before it reaches ground

Answers

Hi there! :)

\(\large\boxed{38.34 m/s}\)

Use the following kinematic equation to solve:

\(v_{f}^{2} = v_{i}^{2} + 2ad\)

Where:

vf = final velocity (?)

vi = initial velocity (0 m/s, object started at rest)

a = acceleration (gravity = 9.8 m/s)

d = distance travelled (75 m)

Plug in the given values into the equation:

\(v_{f}^{2} = 0^{2} + 2(9.8)(75)\)

Simplify:

\(v_{f}^{2} = 2(9.8)(75)\\\\v_{f}^{2} = 1470\)

Take the square root of both sides:

\(v_{f} = \sqrt{1470} = 38.34 m/s\)

I will give BRAINLIEST.... ln the diagram below the system is in equilibrium. Determine the value of F1 in Newton​

I will give BRAINLIEST.... ln the diagram below the system is in equilibrium. Determine the value of

Answers

Answer:

35N

Explanation:

if its balanced both sides would have equal forces. Left side is 35N and right side is 70N. 70-35=35N

brainliest

What technique did astronomers use to make the first confirmed discovery of a planet around another star like the sun?.

Answers

The radial velocity approach is a long-established method in astronomy. Radial velocity was used to discover the first planet ever discovered orbiting a sun-like star.

The discovery was made with the same telescope. The radial velocity approach, which gauges the motion of host stars in response to gravitational tugs from their planets, has proven to be by far the most effective way for discovering and understanding extrasolar planets. The Doppler approach is a reliable way to find exoplanets. It examines the velocity and characteristics of the star and planet using the Doppler effect. The star and the planet both revolve around the same mass. According to the available data, Earth-like planets are the most prevalent type of planet.

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the _____ of the microscope holds and allows selection of the objective lenses.

Answers

The main answer to the given question is that the nosepiece of the microscope holds and allows selection of the objective lenses. It is also known as the turret, and it is a part of a compound microscope.

The turret or nosepiece is a rotating circular disk that holds multiple objective lenses. It rotates on an axis, and each objective lens is brought into place when required.The objective lenses are the most critical part of the microscope. They are located near the specimen and collect light, allowing us to see the magnified image. Typically, a microscope has several objective lenses, ranging in magnification from low to high.

To adjust the focus, one must switch between the objective lenses as required. This is done using the nosepiece or turret.The conclusion of the above answer is that the nosepiece of the microscope is the part that holds and allows selection of the objective lenses. The objective lenses collect light and allow us to view the magnified image.

The nosepiece or turret, which is a rotating circular disk, is used to switch between the objective lenses as required.

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How many gallons can be stored in pressurized horizontal tanks?A. 10 or lessB. 10 to 100C. 100 to 1000D. More than 1000

Answers

The answer to this question depends on the size of the pressurized horizontal tanks. Tanks can vary in size from small portable tanks to large industrial tanks. Small portable tanks that are used for things like propane or camping fuel may hold 10 gallons or less, while larger industrial tanks used for storing chemicals or liquids can hold thousands of gallons.

In general, tanks that fall into the 100 to 1000 gallon range are commonly used for residential or small commercial applications. However, it is important to note that the maximum capacity of a tank will depend on factors such as its design, materials, and intended use. Therefore, it is best to consult the manufacturer or a qualified professional to determine the specific capacity of a pressurized horizontal tank.

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One day, five- year old barbara was running down the street. As she opened the gate to her friends yard, a big dog jumped out and bite her. She was terribly startled and cried out in pain. She now cries whenever she sees any dog

Answers

Answer:

instinct

Explanation:

he charge carriers continue to separate until the magnetic force exactly balances the electric force generated by the newly created electric field. at this equilibrium condition, what is the strength of the electric field e ?

Answers

The strength of the electric field e at the equilibrium condition can be calculated using the equation e = vB, where v is the velocity of the charge carriers and B is the strength of the magnetic field.

When charge carriers move through a magnetic field, they experience a force given by the equation F = qvB, where q is the charge on the carriers, v is their velocity, and B is the strength of the magnetic field.

As a result of this force, the charge carriers move in a circular path. However, as they move, they create an electric field in the direction opposite to their motion, which tries to separate them. This electric field generates an electric force given by the equation F = qE, where E is the strength of the electric field.

The charge carriers continue to separate until the magnetic force exactly balances the electric force. At this equilibrium condition, we have: F = F  qE = qvB  Solving for E, we get: E = vB.

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6. A book that weighs 48N and is lifted 11.6m from the floor to a tabletop. How much work is required to
accomplish this task?

Answers

When work=Force x distance
Therefore,48x11.6= 556.8 joule

I need the answer asap
A man who weighs 75 kg is on the surface of the earth. If the mass of the earth is 6x10^24 kg and its radius 6380 km, calculate the force of attraction between them.
\(mass \: of \: the \: earth \: = 6 \times {10}^{24} \)

[Ans: 737.47 N]

Answers

The force of attraction between the two objects can be calculated using Newton's Law of Universal Gravitation:
F = G m1m2 /r^2
where G is the gravitational constant (6.67x10^-11 Nm^2/Kg^2) m1 is the mass of the man (75 kg) m2 is the mass of the earth (6x10^24 kg) and r is the radius of the earth (6380 km).
Therefore, F = (6.67x10^-11 Nm^2/Kg^2) x (75 kg) x (6x10^24 kg) / (6380 km)^2 = 737.47 N

when information is encoded in molecules, the reproduction cost is _____ than it would be if the information were encoded in bits.
Lower
None of these
higher

Answers

Encoding information in molecules is more higher than encoding information in bits.

When information is encoded in molecules, the reproduction cost is generally higher because it requires more materials and resources to create each encoded molecule. For example, if information is encoded in DNA, then the cost of synthesizing a single strand of DNA is much higher than the cost of storing a single bit in electronic memory. The cost of reproducing the encoded DNA is also much higher than that of reproducing a bit. Additionally, when information is encoded in molecules, the accuracy of the encoded data is often lower than what is possible with digital encoding, which relies on reliable and repeatable computations.

Thus, for these reasons, the cost of reproducing information encoded in molecules is higher than reproducing information encoded in bits.

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What can happen if a body moves through speed of light

Answers

As waves travel into the denser medium, they slow down and wavelength decreases.

Explanation:

The denser the medium the slower the waves (speed of light) travels.

◦•●◉✿When the body approaches the speed of light, the body's length appears to contract in the direction of travel, and its mass appears to increase from the point of view of a stationary observer. Only photons move to light velocity. They don´t have length.✿◉●•◦

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