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amid [387]
3 years ago
7

A scientist notices that an oil slick floating on water when viewed from above has many different colors reflecting off the surf

ace, making it look rainbow-like (an effect known as iridescence). She aims a spectrometer at a particular spot and measures the wavelength to be 750 nmnm (in air). The index of refraction of water is 1.33.
a. The index of refraction of the oil is 1.20. What is the minimum thickness ttt of the oil slick at that spot?
b. Suppose the oil had an index of refraction of 1.50. What would the minimum thickness be now?
c. Now assume that the oil had a thickness of 200 nm and an index of refraction of 1.5. A diver swimming underneath the oil slick is looking at the same spot as the scientist with the spectromenter. What is the longest wavelength of the light in water that is transmitted most easily to the diver?
Physics
1 answer:
Elan Coil [88]3 years ago
5 0

Answer:

(a) 313nm

(b) 250nm

(c) 301nm

Explanation:

This problem involves the concept of thin-film interference. The scientist observes constructive interference. In this case m = 1.

(a) To find the thickness of the oil at that spot we need to first calculate the wavelength in the oil.

       λ = λo/n = 750/ 1.20 = 625nm

λ = wavelength in the material of interest into which light is entering (the oil)

λo = wavelength in the material from which light is coming in or entering.

n = refractive index of the material into which the light is entering.

Light travels from air into the oil. So the refractive index used above is that of the oil and not air.

The formula relating the thickness t to the wavelength is 2t = mλ

m = 1 so,

    2t = λ = 625nm

     t = 625/2 = 313nm

(b) Supposing the refractive index of the water is now n = 1.50

The wavelength in the oil λ = 750/1.50 = 500nm

 The thickness t = λ/2 = 500/2 = 250nm

(c) If the oil has a thickness of 200nm then the wavelength λ = 2t = 2 ×200nm = 400nm

The wavelength in the oil is 400nm. In order to find the wavelength in water we set this wavelength to λo = 400nm. So the wavelength in water seen by the diver is given by the formula

       λ = λo/n

n for water is 1.33

      λ = 400/1.33 = 300.8nm ≈ 301nm.

You might be interested in
You treat 9.540 g of the mixture with the acid and isolate 9.355 g of nacl. what is the weight percent of each substance in the
Mila [183]

The weight percentage of sodium carbonate in the mixture is = 67.71%  

The weight percentage of sodium bicarbonate in the mixture is = 32.57%

<h3>What does "molar mass" ?</h3>

The total mass throughout grams of all the atoms needed to form a molecule per mole is what makes up the molar mass, also known as the molecular weight. Grams per mole is the unit measuring molar mass.

<h3>According to the given information:</h3>

The interaction between sodium carbonate and hydrochloric acid has the following equation:

Na₂CO₃ + HCl  --> NaCl  + CO₂ + H₂O

The reaction's balanced equation is,

Na₂CO₃ + 2HCl  --> 2NaCl  + CO₂ + H₂O -------(2).

When sodium hydrogen carbonate as well as hydrochloric acid react, the following equation results.

NaCO₃ + HCl  --> NaCl  + CO₂ + H₂O ----------------(3)

The Molar mass :

Na₂CO₃ = 106g/mol

NaCO₃ = 84g/mol

NaCl  = 58.5g/mol

The mass of the mixture is Na₂CO₃/NaCO₃ = 9.540g

The molar masses of the constituent elements that make up the compounds are added to determine the molar weight of the substances. In both chemical equations (2) and (3), the unitary technique is employed to calculate the mass of the mixture based on the number of moles (3).

The mass of the sodium carbonate and sodium bicarbonate is calculated with the help of the mass of NaCl formed by the mixture of  Na₂CO₃/NaCO₃ with HCl.

The mixture has the following percentage of sodium carbonate:

        % of Na₂CO₃ =  \frac{x \times 106}{9.540} \times 100\\

                             =\frac{0.061 \times 106}{9.540} \times 100

                             = (6.46/9.540)*100

                             = 67.71%        

The weight percentage of sodium carbonate in the mixture is = 67.71%      

The mixture has the following percentage of NaHCO3:

        % of NaHCO₃ =  \frac{y \times 84}{9.540} \times 100

                             = =\frac{0.037 \times 84}{9.540} \times 100

                              = (3.108/9.540)*100

                             = 32.57%

The weight percentage of sodium bicarbonate in the mixture is = 32.57%

To know more about molar mass visit:

brainly.com/question/12127540

#SPJ4

I understand that the question you are looking for is:

A mixture of sodium carbonate and sodium hydrogen carbonate is treated with aqueous hydrochloric acid. the unbalanced equations for the resulting's reactions are:

Na2CO3 (s) + HCl (aq) --> NaCl (aq) + CO2(g) + H2O (l)

NaHCO3(s) + HCl (aq) --> NaCl (aq) + CO2(g) + H2O (l)

You treat 9.540g of Na2CO3/NaHCO3 mixture with an excess of aqueous HCl and isolate 9.355g of NaCl. What is the weight percent of each substance in the mixture?

5 0
1 year ago
At time t = 1, a particle is located at position (x, y) = (5, 2). If it moves in the velocity field F(x, y) = xy − 1, y2 − 11 fi
Amanda [17]

Answer:

Its approx location is (5.18,1.9)

Explanation:

Using F( 5,2) = ( xy-1, y²-11)

= ( 5*2-¹, 2²-11)

= (9,-5)

= so at point t=1.02

(5,2)+(1.02-1)*(9,-5)

(5,2)+( 0.02)*(9,-5)

(5+0.18, 2-0.1)

= ( 5.18, 1.9)

3 0
3 years ago
28. Which of the following correctly shows the order of highest amount of friction to the lowest amount of
Bad White [126]

Answer:

\mathrm{d.\:Static,\: Sliding,\:Rolling}

Explanation:

Static friction occurs when an object initially starts at rest. When the surfaces of the materials touch, the microscopic unevenness interlock greatest with each other, causing the most friction out of the three.

During sliding friction, an object is already moving or in motion. The microscopic surfaces still interlock, but because the object is in motion, it has a momentum. Therefore, the magnitude of sliding friction is less than that of static friction.

Rolling friction occurs when an object rolls across some surface. Rather than surfaces interlocking, rolling friction is caused by the constant distortion of surfaces. As it rolls, the surfaces of the object are constantly wrapping and changing. This distortion causes the rolling friction. However, it is much less in magnitude when compared to static or sliding friction.

4 0
3 years ago
Ill give 15 points to the one who helps me with this
alexandr402 [8]
Machenical number one
6 0
3 years ago
A 4.44 l container holds 15.4 g of oxygen at 22.55°c. what is the pressure?
padilas [110]
We will use the ideal gas equation:
PV = nRT, where n is moles and equal to mass / Mr
P = mRT/MrV
P = 15.4 x 8.314 x (22.55 + 273) / 32 x 4.44
P = 266.3 kPa
5 0
4 years ago
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