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Sholpan [36]
3 years ago
9

Irina finds an unlabeled box of fine needles, and wants to determine how thick they are. A standard ruler will not do the job, a

s each needle is less than a millimeter thick. So, to find the thickness, she uses a needle to poke a hole in a piece of brown construction paper. Then, she positions a 640 nm laser pointer to shine through the hole and project a circular diffraction pattern on a wall 21.7 m away. She then uses her ruler to measure that the central bright circle is 14.2 cm in diameter. What diameter does Irina calculate for the needle?
Physics
1 answer:
Vsevolod [243]3 years ago
8 0

Answer:

d=\frac{1.22\times 640\times 10^{-9}\times 21.7}{7.35\times 10^{-2}}=2305.21\times 10^{-7}m

Explanation:

The expression which represent the first diffraction minima by a circular aperture is given by d sin\Theta =1.22\lambda--------eqn 1

The angle through which the first minima is diffracted is given by tan\Theta =\frac{y_1}{D}---------eqn 2

As \Theta is very small so we can write sin\Theta =tan\Theta

So from eqn 1 and eqn 2 we can write

y_1=\frac{1.22\lambda D}{d}--------eqn 3

Here y_1 is the position of first maxima D is the distance of screen from the circular aperture d is the diameter of aperture

It is given that diameter of circular aperture is 14.7 cm so y_1=\frac{14.7}{2}=7.35 \ cm

Now putting all these value in eqn 3

d=\frac{1.22\lambda D}{y_1}

d=\frac{1.22\times 640\times 10^{-9}\times 21.7}{7.35\times 10^{-2}}=2305.21\times 10^{-7}m

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Thermopane window is constructed, using two layers of glass 4.0 mm thick, separated by an air space of 5.0 mm.
Bond [772]

To solve this problem it is necessary to apply the concepts related to rate of thermal conduction

\frac{Q}{t} = \frac{kA\Delta T}{d}

The letter Q represents the amount of heat transferred in a time t, k is the thermal conductivity constant for the material, A is the cross sectional area of the material transferring heat, \Delta T, T is the difference in temperature between one side of the material and the other, and d is the thickness of the material.

The change made between glass and air would be determined by:

(\frac{Q}{t})_{glass} = (\frac{Q}{t})_{air}

k_{glass}(\frac{A}{L})_{glass} \Delta T_{glass} = k_{air}(A/L)_{air} \Delta T_{air}

\Delta T_{air} = (\frac{k_{glass}}{k_{air}})(\frac{L_{air}}{L_{glass}}) \Delta T_{glass}

\Delta T_{air} = (\frac{0.84}{0.0234})(\frac{5}{4}) \Delta T_{glass}

\Delta T_{air} = 44.9 \Delta T_{glass}

There are two layers of Glass and one layer of Air so the total temperature would be given as,

\Delta T = \Delta T_{glass} +\Delta T_{air} +\Delta T_{glass}

\Delta T = 2\Delta T_{glass} +\Delta T_{air}

20\°C = 46.9\Delta T_{glass}

\Delta T_{glass} = 0.426\°C

Finally the rate of heat flow through this windows is given as,

\Delta {Q}{t} = k_{glass}\frac{A}{L_{glass}}\Delta T_{glass}

\Delta {Q}{t} = 0.84*24*10 -3*0.426

\Delta {Q}{t} = 179W

Therefore the correct answer is D. 180W.

3 0
3 years ago
The function​ s(t) represents the position of an object at time t moving along a line. Suppose s (2 )equals 146and s (6 )equals
sineoko [7]

Answer:

v(t) = 27 units

Explanation:

The function s(t) represents the position of an object at time t moving along a line such that,

s(2)=146

and

s(6)=254

We need to find the average velocity of the object over the interval of time [2,6]. The velocity of the object is equal to the total distance divided by time. It is given by :

v(t)=\dfrac{s(6)-s(2)}{6-2}

v(t)=\dfrac{254-146}{6-2}

v(t) = 27 units

So, the  average velocity of the object is 27 units. Hence, this is the required solution.

5 0
3 years ago
Explain how the data collected and the calculations for the first and second resonance points in today's experiment would change
grandymaker [24]

Answer:

tssths

Explanation:

hgst

8 0
3 years ago
a man pushes on a wall with a force of 50N. what are the size and direction of the force that the wall exert on the man?
Ira Lisetskai [31]
According to Newton's 3rd law of motion, every action has an equal and opposite reaction. So Wall must apply a force of 50 Newton but in opposite direction. Hope you got it :-D
5 0
3 years ago
The current in a resistor is 3.0 A, and its power is 60 W. What is the voltage?
Novosadov [1.4K]

Answer:

20 volts

Explanation:

Use the equation P=VI

60=V(3)

V=20

6 0
2 years ago
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