Magnesium fluoride MgF2 has n = 1.37. If applied in a thin layer over an optical lens made of glass having n = 1.39, what thickness should it be so that light having a wavelength of 645 nm is not reflected from the lens?

Answers

Answer 1

SOLUTION:
We want to choose the film thickness such that destructive interference occurs between the light reflected from the air-film interface (call it wave 1) and from the film-lens interface (call it wave 2). For destructive interference to occur, the phase difference between the two waves must be an odd multiple of half-wavelengths.
You can think of the phases of the two waves as second hands on a clock; as the light travels, the hands tick-tock around the clock. Consider the clocks on the two waves in question. As both waves travel to the air-film interface, their clocks both tick-tock the same time-no phase difference. When wave 1 is reflected from the air-film boundary, its clock is set forward 30 seconds; i.e., if the hand was pointing toward 12, it's now pointing toward 6. It's set forward because the index of refraction of air is smaller than that of the film.
Now wave 1 pauses while wave two goes into and out of the film. The clock on wave 2 continues to tick as it travels in the film-tick, tock, tick, tock.... Clock 2 is set forward 30 seconds when it hits the film-lens interface because the index of refraction of the film is smaller than that of the lens. Then as it travels back through the film, its clock still continues ticking. When wave 2 gets back to the air-film interface, the two waves continue side by side, both their clocks ticking; there is no change in phase as they continue on their merry way.
So, to recap, since both clocks were shifted forward at the two different interfaces, there was no net phase shift due to reflection. There was also no phase shift as the waves travelled into and out from the air-film interface. The only phase shift occured as clock 2 ticked inside the film.
Call the thickness of the film t. Then the total distance travelled by wave 2 inside the film is 2t, if we assume the light entered pretty much normal to the interface. This total distance should equal to half the wavelength of the light in the film (for the minimum condition; it could also be 3/2, 5/2, etc., but that wouldn't be the minimum thickness) since the hand of the clock makes one revolution for each distance of one wavelength the wave travels (right?).
\begin{displaymath}
2t = \frac{\lambda_{film}}{2}.\end{displaymath}

The wavelength in the film is

\begin{displaymath}
\lambda_{film} = \frac{\lambda_{air}}{n} = \frac{565 nm}{1.38}\end{displaymath}

\begin{displaymath}
\lambda_{film} = 409 nm.\end{displaymath}

Hence, the thickness should be

\begin{displaymath}
t = \frac{\lambda_{film}}{4} = 102 nm .\end{displaymath}

Answer 2

so the answer is I am so confuse

Related Questions

Madison lives near the ocean. She’s formed a hypothesis that increased concentrations of salt in the air speeds the corrosion of certain metals. If Madison plans to test this hypothesis, she will have to deal with the following variables in her experiment:

Answers

The variables that Madison will have to deal with to test her hypothesis that increased concentrations of salt in the air speeds the corrosion of certain metals are as follows:

Independent variable: concentration of saltDependent variable: corrosion of metal

What are independent and dependent variables?

In an experiment, the independent variable is the variable that is changed or manipulated in a series of experiments.

On the other hand, a dependent variable is that outcome measured to see the effectiveness of the treatment.

According to this question, Madison makes an hypothesis that an increased concentrations of salt in the air speeds the corrosion of certain metals, the variables she should look out for are as follows:

Independent variable: concentration of saltDependent variable: corrosion of metal

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Q15.17 Both wave intensity and gravitation obey inverse-square laws. Do they do so for the same reason?Discuss the reason for each of these inverse-square laws as well as you can. block is attached to an ideal spring and is mov ing in SHM on a horizontalfrictionless surfaceThe amplitude of the motion is 0.120 m.The maximum speed of the block is 3.90 m/s.What is the maximum magnitude of the acceleration of the block?

Answers

(a) Intensity obeys inverse square law from basis of light passing through a given surface.

(b) Gravitation obeys inverse square law from the basis of force between two masses.

What is intensity?

Intensity is the ratio is ratio of power to area of a given surface.

I = P/A (W/m²)

where;

P is powerA is areaUniversal gravitation law

[tex]F = \frac{Gm_1m_2}{r^2}[/tex]

Intensity and gravitation do not obey inverse square law for same reason;

Intensity obeys inverse square law from basis of light passing through a given surface.Gravitation obeys inverse square law from the basis of force between two masses.Acceleration of the block

a = v²/A

a = (3.9²)/0.12

a = 126.75 m/s²

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Help me with the following problem

Answers

(a) The value of charge q3 when the total potential is 0, is determined as -1.7 μC.

(b) The value of charge q3 when the total potential is 290 kV, is determined as -0.255 μC.

Electric potential of the charges

The electric potential of a charge at any distance r is calculated as follows;

V = Kq/r

V = k(q₁/r₁ + q₂/r₂ + q₃/r₃)

when the potential, V = 0

0 = k(q₁/r₁ + q₂/r₂ + q₃/r₃)

0 = q₁/r₁ + q₂/r₂ + q₃/r₃

0 = 9.3/4.5 - 4.9/2.9 + q₃/4.5

0 = 0.377 + q₃/4.5

q₃/4.5 = -0.377

q₃ = 4.5 x (-0.377)

q₃ = -1.7 μC

When the potential, V = 290 kV

V = k(q₁/r₁ + q₂/r₂ + q₃/r₃)

290,000 = k(q₁/r₁ + q₂/r₂ + q₃/r₃)

[tex]\frac{290,000}{9\times 10^9} = \frac{9.3 \times 10^{-6}}{0.045} - \frac{4.9\times 10^{-6}}{0.029} + \frac{q_3}{0.029} \\\\3.22 \times 10^{-5} = 2.1 \times 10^{-4} -1.69 \times 10^{-4} + \frac{q_3}{0.029} \\\\3.22 \times 10^{-5} = 4.1 \times 10^{-5} + \frac{q_3}{0.029}\\\\-8.8 \times 10^{-6} = \frac{q_3}{0.029}\\\\q_3 = -2.55 \times 10^{-7}\\\\q_3 = -0.255 \times 10^{-6}\\\\q_3 = -0.255 \ \mu C[/tex]

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An object weighs 200N on earth What would be its mass on the moon

Answers

The mass is the same no matter where the object is, but the weight on the moon changes because gravity is weaker there. So the mass is m = 20N/9.81 m/s^2 = 2.04kg

Mass will be same on moon as it was on earth

What is mass ?

Mass is the measure of inertia or the amount of matter in body .It is a property of matter .

since, it is a property of matter and we know that amount of matter will remain same no matter the place . Amount of matter will same even at moon as it was on earth .

hence , mass will remain same irrespective of place

It will be same on moon as it was on earth

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Gerard is measuring the speed of a remote-controlled airplane. He measures that the airplane travels 110 m in 5.4 seconds, giving a speed of 20 m/s. What will Gerard need to change, if he wants to get a more precise value for speed

Answers

Gerard need to change the Acceleration.

What is speed?

Speed is defined as the distance travelled by an object in a unit time.

Mathematically ,

Speed =[tex]\frac{Distance}{Time}[/tex]

Here the given values are:

Distance = 110m and time = 5.4 s

Speed = [tex]\frac{110}{5.4}[/tex] = 20 m/s

For increasing the speed he need to change the acceleration.

Which is define as the rate at which velocity changes with time, in terms of both speed and direction.

Any change in the velocity of an object results in an acceleration , increasing speed (what people usually mean when they say acceleration).

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If cholesterol buildup reduces the diameter of an artery by 21 % , by what % will the blood flow rate be reduced, assuming the same pressure difference?

Answers

Assuming the same pressure difference, the blood flow rate will be reduced by 49%.

Reduction of the blood flow rate

Volumetric flow rate is calculated as follows;

Q = V/t

Q = πr³/t

r = d/2

r³ = d³/8

Q = πd³/8t

Q = ¹/₈ πd³/t

Q₁/d₁³ = Q₂/d₂³

Q₂ = d₂³(Q₁/d₁³)

d₂ = 100%d₁ - 21%d₁ = 79%d₁

Q₂ = (0.79d₁)³(Q₁/d₁³)

Q₂ = 0.49d₁³(Q₁/d₁³)

Q₂ = 0.49Q₁

Q₂ = 49%

Thus, assuming the same pressure difference, the blood flow rate will be reduced by 49%.

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A car is moving at a constant speed along a straight line. Which statement is true about the forces acting on the car?

Answers

The statement that is true about the forces acting on the car is that the net force acting on the car from all directions is zero. Option A is correct.

What is force?

Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body.

The complete question is

"A car is moving at a constant speed along a straight line. Which statement is true about the forces acting on the car?

The net force acting on the car from all directions is zero.

The net force acting on the car is greater than the car's weight.

The net force acting on the car is in the direction of the car's motion.

The net force acting on the car is in the opposite direction of the car's motion."

The net force operating on the automobile in all directions is zero,

The statement that is true about the forces acting on the car is that the net force acting on the car from all directions is zero. Option A is correct.

Hence option A is correct.

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Which of the following energy sources is not used in California? A. coal B. natural gas C. nuclear wind

Answers

Answer:

coal

Explanation:

Given the vectors a=6m west and b=11 m south using graphical method determine which of the following most likely represent the magnitude and direction of the difference vector a-b respectively

Answers

66666 and yw a and yes let’s

Question 20 (4 points)
Listen
When a net horizontal force of 250 N acts on a 50-kg cart that is free to roll on a
level surface,
A) the cart accelerates at 9.8 m/s².
B)
the cart accelerates at 0.20 m/s².
C)
the cart accelerates at 5 m/s².
D)
the cart accelerates at 12500 m/s².
E)
the cart does not accelerate because it pushes back on the person with a
force of 250 N.

Answers

Explanation:

C is correct.

Newton second law states that force is directly proportional to acceleration with m being the constant of variation.

[tex]f _{net} = m(a)[/tex]

[tex]250 = 50(a)[/tex]

[tex]a = 5[/tex]

A is wrong, the constant g only happens in free fall or in vertical direction

B and D are wrong due to the mathematical error or equation error

When ice melts at 0C its volume decreases. Is the internal energy change greater than, less than, or equal to the heat added? How can you tell?

Answers

In this case W is negative, the heat input is less than in the constant volume case, and CP is less than CV. If the ice melts it is as if it were being compressed because its volume is reduced.

MyHeritage

Calculate the vertical component with the magnitude of 33km with an angle of 140 degrees

Answers

The answer is 31.84

The vertical component with the magnitude of 33km with an angle of 140 degrees

Here ,

90 -θ = 140

θ = 50

By the given formula of vertical component

a = h x cos θ

a = 33 x cos (50)

a = 31.84

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