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White raven [17]
2 years ago
5

21.13 The index of refraction of corundum (Al2O3) is anisotropic. Suppose that visible light is passing from one grain to anothe

r of different crystal-lographic orientation and at normal incidence to the grain boundary. Calculate the reflectivity at the boundary if the indices of refraction for the two grains are 1.757 and 1.779 in the direction of light propagation.
Engineering
1 answer:
d1i1m1o1n [39]2 years ago
6 0

Answer:

3.87 x 10⁻⁵

Explanation:

Given parameters

normal incidence

refraction index of grain1, n₁ = 1.757

refraction index of grain2, n₂ = 1.779

to calculate reflectivity index between the two grains of different orientation an at normal incidence, we use the relation

R = [\frac{n2 - n1}{n2 + n1} ]^{2}

since the incidence is normal where R, is the index of relativity

R = [\frac{1.779 - 1.757}{1.779 + 1.757} ]^{2}

R = 3.87 x 10⁻⁵

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A railcar with an overall mass of 78,000 kg traveling with a speed vi is approaching a barrier equipped with a bumper consisting
sergij07 [2.7K]

Answer:

v₀ = 2,562 m / s  = 9.2 km/h

Explanation:

To solve this problem let's use Newton's second law

              F = m a = m dv / dt = m dv / dx dx / dt = m dv / dx v

              F dx = m v dv

We replace and integrate

            -β ∫ x³ dx = m ∫ v dv

            β x⁴/ 4 = m v² / 2

We evaluate between the lower (initial) integration limits v = v₀, x = 0 and upper limit v = 0 x = x_max

        -β (0- x_max⁴) / 4 = ½ m (v₀²2 - 0)

         x_max⁴ = 2 m /β   v₀²

         

Let's look for the speed that the train can have for maximum compression

         x_max = 20 cm = 0.20 m

         

         v₀ =√(β/2m)   x_max²

Let's calculate

          v₀ = √(640 106/2 7.8 104)    0.20²

          v₀ = 64.05  0.04

          v₀ = 2,562 m / s

          v₀ = 2,562 m / s (1lm / 1000m) (3600s / 1h)

          v₀ = 9.2 km / h

5 0
2 years ago
An excited electron in an Na atom emits radiation at a wavelength 589 nm and returns to the ground state. If the mean time for t
11Alexandr11 [23.1K]

Answer:   Inherent width in the emission line: 9.20 × 10⁻¹⁵ m or 9.20 fm

                length of the photon emitted: 6.0 m

Explanation:

The emitted wavelength is 589 nm and the transition time is ∆t = 20 ns.

Recall the Heisenberg's uncertainty principle:-

                                 ∆t∆E ≈ h ( Planck's Constant)

The transition time ∆t corresponds to the energy that is ∆E

E=h/t = \frac{(1/2\pi)*6.626*10x^{-34} J.s}{20*10x^{-9} } = 5.273*10x^{-27} J =  3.29* 10^{-8} eV.

The corresponding uncertainty in the emitted frequency ∆v is:

∆v= ∆E/h = (5.273*10^-27 J)/(6.626*10^ J.s)=  7.958 × 10^6 s^-1

To find the corresponding spread in wavelength and hence the line width ∆λ, we can differentiate

                                                    λ = c/v

                                                    dλ/dv = -c/v² = -λ²/c

Therefore,

      ∆λ = (λ²/c)*(∆v) = {(589*10⁻⁹ m)²/(3.0*10⁸ m/s)} * (7.958*10⁶ s⁻¹)

                                 =  9.20 × 10⁻¹⁵ m or 9.20 fm

     The length of the photon (<em>l)</em> is

l = (light velocity) × (emission duration)

  = (3.0 × 10⁸  m/s)(20 × 10⁻⁹ s) = 6.0 m          

                                                   

6 0
2 years ago
A person puts a few apples into the freezer at -15oC to cool them quickly for guests who are about to arrive. Initially, the app
frosja888 [35]

Answer:

Temperature at center of apples = 11.2⁰C

Temperature at surface of apples = 2.7⁰C

Amount of Heat transferred = 17.2kJ

Explanation:

The properties of apple are given as:

k = 0.418 W/m.°C

ρ = 840 kg/m³

Cр = 3.81 kJ/kg.°C

α = 1.3*10 ⁻⁷ m²/s

h = 8 W/m².°C

d = 0.09m

r = 0.045m

t = 1 hour = 3600s

<h2>Solution</h2>

Biot number is given as:

Bi = \frac{hr}{k}= \frac{8\cdot0.045}{0.418}=0.861

The constants λ₁ and A₁ corresponding to Biot number (from the table) are:

λ₁ = 1.476

A₁ = 1.239

Fourier Number is:

T = \frac{a\cdot{t}}{r^2} = \frac{(1.3\cdot10^{-7})(3600)}{0.045^2}= 0.231> 0.2

As Fourier Number > 0.2 , one term approximates solutions are applicable

The temperature at the center of apples, The temperature at surface of apples and Amount of heat transfer is found in the ATTACHMENT.

8 0
2 years ago
A shipment of rebar that weighs 745 kg would weigh roughly how much in pounds​
Andre45 [30]

Answer:

Dont no but will check

Explanation:

6 0
2 years ago
Consider air entering a heated duct at P1 = 1 atm and T1 = 288 K. Ignore the effect of friction. Calculate the amount of heat pe
Ne4ueva [31]

Answer:

The solution for the given problem is done below.

Explanation:

M1 = 2.0

\frac{p1}{p*} = 0.3636

\frac{T1}{T*} = 0.5289

\frac{T01}{T0*} = 0.7934

Isentropic Flow Chart:  M1 = 2.0 , \frac{T01}{T1} = 1.8

T1 = \frac{1}{0.7934} (1.8)(288K) = 653.4 K.

In order to choke the flow at the exit (M2=1), the above T0* must be stagnation temperature at the exit.

At the inlet,

T02= \frac{T02}{T1}T1 = (1.8)(288K) = 518.4 K.

Q= Cp(T02-T01) = \frac{1.4(287 J / (Kg.K)}{1.4-1}(653.4-518.4)K = 135.7*10^{3} J/Kg.

5 0
2 years ago
Read 2 more answers
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