Ask question

Ask question

All categories

3 years ago

8

Biologists use optical tweezers to manipulate micron-sized objects using a beam of light. In this technique, a laser beam is foc

used to a very small-diameter spot. Because small particles are attracted to regions of high light intensity, the focused beam can be used to "grab" onto particles and manipulate them for various experiments. In one experiment, a 10 mW laser beam is focused to a spot that has a diameter of 0.67 μm
Part A: What is the intensity of the light in this spot?

Part B: What is the amplitude of the electric field?

1 answer:

vekshin13 years ago

8 0

Answer:

Explanation:

Part A) Using

light intensity I= P/A

A= Area= π (Radius)^2= π((0.67*10^-6m)/(2))^2= 1.12*10^-13 m^2

Radius= Diameter/2

P= power= 10*10^-3=0.01 W

light intensity I= 0.01/(1.12*10^-13)= 9*10^10 W/m^2

Part B) Using

I=c*ε*E^2/2

rearrange to solve for E= $\sqrt{$ ((I*2)/(c*ε))

c is the speed of light which is 3*10^8 m/s^2

ε=permittivity of free space or dielectric constant= 8.85* 10^-12 F⋅m−1

I= the already solved light intensity= 8.85*10^10 W/m^2

amplitude of the electric field E= $\sqrt{$ (9*10^10 W/m^2)*(2) / (3*10^8 m/s^2)*(8.85* 10^-12 F⋅m−1)

---> E= $\sqrt{$ (1.8*10^11) / (2.66*10^-3) = $\sqrt{$ (6.8*10^13) = 8.25*10^6 V/m

You might be interested in

Can somebody please explain how a compass can be used to find North?

Ira Lisetskai [31]

if the pointy thingy in your compass is pointing north, that means it's being (pulled toward) something near Earth's north pole

5 0

3 years ago

Three identical very dense masses of 7500 kg each are placed on the x axis. One mass is at x1 = -100 cm , one is at the origin,

sukhopar [10]

Answer:

0.00354 (N)

Explanation:

Convert to metric system:

$x_1 = -100 cm = 1 m$

$x_2 = 420 cm = 4.2 m$

Formula for gravitational force:

$F_g = G\frac{mM}{s^2}$

where s is the distance between 2 bodies masses m and M

Substitute the number to the formula above and since the 2 forces are acting in opposite direction, the total net gravitational force on the mass of origin be:

$F_g = F_{g1} - F_{g2}$

$F_g = G\frac{m_1M}{x_1^2} - G\frac{m_2M}{x_2^2}$

$F_g = GM(\frac{m_1}{x_1^2} - \frac{m_2}{x_2^2})$

$F_g = 6.67*10^{-11} * 7500 (\frac{7500}{1^2} - \frac{7500}{4.2^2})$

$F_g = 5*10^{-7}(7500 - 425.17)$

$F_g = 5*10^{-7} * 7074.83$

$F_g = 0.00354 (N)$

5 0

3 years ago

Determine the speed of sound in air at 300 K. Also determine the Mach number of an aircraft moving in the air at a velocity of 3

amm1812

Answer:

$c_3_0_0_K=347.19m/s$

$M=0.864$

Explanation:

The speed of sound in the air increases 0.6 m / s for every 1 ° C increase in temperature. An approximate speed can be calculated using the following empirical formula:

$c=331.5+0.6\vartheta$

Where:

$\vartheta=T-273.15K\\\\$

A more exact equation, usually referred to as adiabatic velocity of sound, is given by the following formula:

$c=\sqrt{k*R*T}$

Where:

$R= Gas\hspace{3}constant\hspace{3}of\hspace{3}air=0.287kJ/kg*K=287J/kg*K\\k=Specific\hspace{3}heat\hspace{3}ratio=1.4\\T=Temperature=300K$

Hence:

$c=\sqrt{(287)*(1.4)*(300)} =347.1887095\approx347.19m/s$

Now, the Mach number at which an aircraft is flying can be calculated by:

$M=\frac{u}{c}$

Where:

$u= Velocity\hspace{3}of\hspace{3}the\hspace{3}moving\hspace{3}aircraft\\c= Speed\hspace{3}of\hspace{3}sound\hspace{3}at\hspace{3}the\hspace{3}given \hspace{3}altitude$

Therefore:

$M=\frac{300}{347.19} =0.8640833984\approx0.864$

5 0

4 years ago

KI + Cl2 ---> KCl + I2<br> Balance the single replacement chemical reaction.

snow_lady [41]

Answer:

2KI + Cl₂ → 2KCl + I₂

Explanation:

The reaction equation is given as:

KI + Cl₂ → KCl + I₂

The problem at hand is to balance this chemical reaction. To solve this problem we use a mathematical approach;

aKI + bCl₂ → cKCl + dI₂

Conserving K : a = c

I : a = 2d

Cl : 2b = c

Now let a = 1, c = 1 , d = $\frac{1}{2}$ , b = $\frac{1}{2}$ , ;

Multiply through by 2;

a = 2, b = 1 , c = 2, d = 1

2KI + Cl₂ → 2KCl + I₂

5 0

3 years ago

Select the best answer.<br> When was traditional chemistry started?

sergejj [24]

17th Century
In 1661 he founded a scientific society which later became known as the Royal Society of England. Traditional Chemistry - The Mid 17th Century to mid 19th Century By this time scientists were using the "modern method" of discovery by testing theories with experiments.

8 0

3 years ago