A physics student mounts two thin lenses along a single optical axis (the lenses are at right angles to the line connecting them, and they appear concentric when viewed from either end). The lenses are identical, each with a positive (converging) focal length of 14.8 cm. They are separated by a distance of 39.4 cm. Lens 1 is to the left of Lens 2.
Required:
a. What is the final image's distance (in cm) from Lens 2?
b. Where is the final image located?
c. What is the overall magnification of the lens pair, considered as a single optical instrument?
Answer:
A) q₂ = 75.98 cm, B) q₂' = 115.38 cm, C)
Explanation:
A) This is an exercise in geometric optics, as the two lenses are separated by a greater distance than their focal lengths from each lens, they must be worked as independent lenses.
Lens 1. More to the left
let's use the constructor equation
[tex]\frac{1}{f} = \frac{1}{p} + \frac{1}{q}[/tex]
where f is the focal length, p and q are the distance to the object and the image, respectively,
We must assume a distance to the object to perform the calculation, suppose that the object is 50 cm from lens 1 that is further to the left of the system.
[tex]\frac{1}{q_1} = \frac{1}{f} - \frac{1}{p}[/tex]
[tex]\frac{1}{q_1} = \frac{1}{14.8} - \frac{1}{50}[/tex]
1 / q₁ = 0.04756
q₁ = 21.0227 cm
this image is the object for the second lens that has f₂ = 14.8 cm
the distance must be measured from the second lens
p₂ = 39.4 -q₁
p₂ = 39.4 -21.0227
p₂ = 18.38 cm
let's use the constructor equation
1 / q₂ = 1 / f - 1 / p2
[tex]\frac{1}{q_2} = \frac{1}{14.8} - \frac{1}{18.38}[/tex]
[tex]\frac{1}{q_2}[/tex] = 0.01316
q₂ = 75.98 cm
measured from the second lens
B) the position of the final image with respect to the first lens is
q₂’= q₂ + 39.4
q₂'= 75.98 +39.4
q₂' = 115.38 cm
C) the magnification of a lens is
m = - q / p
in this case the image measured from lens 2 is q2 = 75.98 cm
the distance to the object from the first lens is p1 = 50cm
m = - 75.98 / 50
m = -1.5 X
the negative sign indicates that the image is inverted
His eyes are 1.83 m above the floor, and the top of his head is 0.15 m higher. Find the height above the floor of the top and bottom of the smallest mirror in which he can see both the top of his head and his feet.
Answer:
y_lower = 0.915 m, y_superior = 1,905 m
Explanation:
In this exercise we use the law of reflection for a flat mirror.
θ’= θ
To see the feet of the person a ray of light that part of them must reach the bottom of the mirror and its reflection has to reach the eyes.
As the law of reflection the incident and reflected angles are equal, the distance from the floor to the point where the two rays (incident and reflected) touch the mirror must be symmetrical, oses from the floor
y = 1.83 / 2
y = 0.915 m
To see the head, a ray of light that comes from the tip of the head and is reflected in the mirror must reach the eyes. As the head is 0.15 m above the eyes and the incident and reflected rays have the same angle, the mirror must be at half the height, that is, the mirror is 0.075 m below the tip of the head.
In summary
* the bottom of the mirror is 0.915 m from the ground
* the top of the mirror is at 1.83 + 0.075
y_superior = 1,905 m
ground
A 70 kg human body typically contains 140 g of potassium. Potassium has a chemical atomic mass of 39.1 u and has three naturally occurring isotopes. One of those isotopes, 40K (potassium), is radioactive with a half-life of 1.3 billion years and a natural abundance of 0.012 %. Each 40K (potassium) decay deposits, on average, 1.0 MeV of energy into the body.
What yearly dose in Gy does the typical person receive from the decay of 40K (potassium) in the body? Express your answer using two significant figures.
Answer:
Gy = 3.14x10⁻⁴ Gy
Explanation:
To get the dose in Gy we need to use the following expression:
Gy = E / m (1)
Where:
Gy: dose
E: energy absorbed per atom
m: mass of the human body.
We don't have the energy per atom, but we can calculate that by following the next procedure.
First, let's determine the number of atoms of potassium in our body. For that we need to determine the moles in the 140 g of potassium, with the molecular mass and then, use the avogadro's number:
moles = m/MM
moles = 140 / 39.1 = 3.58 moles
N° atoms = 3.58 * 6.02x10²³ atoms = 2.16x10²⁴ atoms of K.
The abundance of the ⁴⁰K is 0.012% so the atoms of this isotope would be:
N = 2.16x10²⁴ * (0.012/100) = 2.59x10²⁰ atoms of ⁴⁰K.
With this number, and the half life rate, we can determine the number of decay atoms in a year (λ) using the following expression:
λ = ln2 / t(1/2)
λ = ln2 / 1.3x10⁹ = 5.33x10⁻¹⁰ year⁻¹
This number, multiplied by the number of atoms:
R = 5.33x10⁻¹⁰ * 2.59x10²⁰ = 1.38x10¹¹ atoms/year
Now, each atom of K gives an average energy of 1 MeV, so with the atoms we have:
E = 1.38x10¹¹ * 1x10⁶ eV = 1.38x10¹⁷ eV
This value can be expressed in Joules so:
E = 1.38x10¹⁷ eV * (1 J / 6.24x10¹⁸ eV) = 0.022 J
Finally, we can use (1) to get the dose in Gy:
Gy = 0.022 / 70
Gy = 3.14x10⁻⁴ GyHope this helps
Which element would have properties most like helium (He)?
A. Ar
B. Hg
C. H
D. O
Answer: A. Ar
Explanation: not anything else besides Ar
The tension in a pulley belt is 31 N when stationary. Calculate power in watts transmitted when the belt is on the point of slipping on the smaller wheel. the wheel is 379 mm diameter and the coefficient of friction is 0.3. The angle of lap is 1610. The wheel speed is 1,547 rev/min.
Answer:
P = 756.84 Watts
Explanation:
As the tension is stationary or innitial, T₀ = 31 N, the mean would be:
T₁ + T₂ / 2 = T₀ (1)
T₁ + T₂ = 2 * 31 = 62 N
Now, with the following expression we can determine the linear speed:
V = πWD (2)
W: angular speed of the wheel (rev/s)
D: diameter of the wheel (in meters)
W = 1547 rev/min * (1 min/60 s) = 25.78 rev/s
V = π * 25.78 * 0.379 = 30.695 m/s
We also know that:
T₁ / T₂ = exp (μθ)
T₁ = T₂ exp(μθ) (3)
We already have those values so replacing:
T₁ = T₂ exp(0.3 * 161 * π/180)
T₁ = 2.32T₂ (4)
We can now replace (4) in (1) like this:
T₁ + T₂ = 62 N
2.32T₂ + T₂ = 62
3.32T₂ = 62
T₂ = 18.67 N
Which means that T₁:
T₁ = 2.32(18.67)
T₁ = 43.33 N
Finally, the power can be determined using the following expression:
P = (T₁ - T₂)V (5) Replacing we have:
P = (43.33 - 18.67)*30.695
P = 756.84 WattsHope this helps
The load across a 12 V battery consists of a series combination of three resistors 34 Ω, 42Ω, and 30Ω. What is the total resistance of the load? Answer in units of Ω. What is the current in the circuit? Answer in units of A.
Answer:
The total resistance is 106 Ω and the current in the circuit is 0.11 A.
Explanation:
Given that,
Voltage of the battery, V = 12 V
Resistors 34 Ω, 42Ω, and 30Ω are connected in series.
The total resistance is given by :}
R = 34 + 42 +30
= 106Ω
Let I is the total current in the circuit. Using ohm's law to find it such that,
[tex]I=\dfrac{V}{R}\\\\I=\dfrac{12}{106}\\\\I=0.11\ A[/tex]
Hence, the total resistance is 106 Ω and the current in the circuit is 0.11 A.
I will mark u brainlist
Answer:
DragonFly or a dog
Explanation:
Perhaps the greatest of the Greek astronomers, Hipparchus compiled the first catalog of stars, 49) accurately measured their positions, and defined the basic system of stellar brightnesses which we now call the magnitude system. A particular star in his catalogue has an apparent magnitude of 4 and an absolute -12. Determine the distance to the star.
Answer:
Explanation:
it would be 3 because ju divide 12 by 4
What is the resistance of a rheostat coil, if 0.05 A of current flows through it when 6 V is applied
across it? 1200
Answer:
i have no idea i came here to find out too :(
Explanation:
Two electromagnetic waves are traveling through empty space. The wave with the greater wavelength is also characterized by _____.
a. the lower frequency
b. the higher frequency
c. the faster speed
d. the slower speed
What is Ship Handling, an art or a science? Why?
Ship handling is both a science and an art. Science because it requires knowledge of various forces acting on the ship. Art because it requires the skills of an experienced navigator to use these forces in his favour. We may learn the science part from the various ship handling courses.
please give brainliest
The first law of thermodynamics (which states that energy is conserved) does not specify the direction in which thermodynamic processes in nature can spontaneously occur.
a. True
b. False
Answer:
a. True
Explanation:
The law of conservation of Energy states that energy cannot be destroyed but can only be converted or transformed from one form to another. Therefore, the sum of the initial kinetic energy and potential energy is equal to the sum of the final kinetic energy and potential energy.
Mathematically, it is given by the formula;
Ki + Ui = Kf + Uf .......equation 1
Where;
Ki and Kf are the initial and final kinetic energy respectively.
Ui and Uf are the initial and final potential energy respectively.
The First Law of Thermodynamics is another way to describe the Law of Conservation of Energy. Typically, the First Law of Thermodynamics states that the change of internal energy of a system is equal to the sum of external work and heat spent on the system.
Mathematically, the First Law of Thermodynamics is given by the formula;
ΔU = Q − W
Where;
ΔU represents the change in internal energy of a system.
Q represents the net heat transfer in and out of the system.
W represents the sum of work (net work) done on or by the system.
Hence, the direction in which any thermodynamic process in nature can spontaneously occur isn't stated by the First Law of Thermodynamics.
A wave has a speed of 450 m/s and a frequency of 5 Hz. What is its wavelength?
Give you answer to a 1 decimal place.
Your Answer:
Answer
the wavelength is 90
Explanation:
a person is sitting on the last bench can see clearly see things written on book but cannot see them distinctly on board. what types of lens is this concave or convex
Answer:
I think concave
Explanation:
A 7.5 cm tall Aragorn action figure is placed 12.4 cm in front of a double convex lens. If the image of Aragorn is located 7.5 from the lens, what is the focal length of the lens?
Answer:
f = 4.67 cm
Explanation:
Here, we can use the thin lens formula, as follows:
[tex]\frac{1}{f}= \frac{1}{p}+ \frac{1}{q}\\\\[/tex]
where,
f = focal length of lens = ?
p = distance of object from lens = 12.4 cm
q = distance of image from lens = 7.5 cm
Therefore,
[tex]\frac{1}{f} =\frac{1}{12.4\ cm} +\frac{1}{7.5\ cm}\\\\\frac{1}{f} = \frac{1}{4.67\ cm}[/tex]
f = 4.67 cm
A uniform electric field exists everywhere in the x,y plane. The electric field has a magnitude of 3500 N/coil, and is directed in the positive x direction. A point charge of -9.0 x 10-9 coil is placed at the origin. Determine the magnitude of the net electric field at: (a) x
Answer:
5525 N/C
Explanation:
Magnitude of electric field ( E ) = 3500 N/c
Direction of electric field : positive X axis
point charge ( q ) = -9.0 * 10^-9
Calculate the Magnitude of the net electric field at (a) x = -0.20 m
Magnitude = 5525 N/C
Electric field due to q = ( 9 * 10^9 * 9 * 10^-9 ) / ( -0.2 )^2
= 81 / 0.04 = 2025 N/c
Therefore the magnitude of the net electric field
= 2025 + 3500
= 5525 N/C
The table shows the relationship between the masses of two objects, the distance between the two objects, and the gravitational force between the objects. A 4-column table with 5 rows. The first column labeled Mass of Object 1 (kilograms) has entries 1, 2, 2, 3, 9. The second column labeled Mass of Object 2 (kilograms) has entries 1, 1, 2, 3, 3. The third column labeled Distance between Objects 1 and 2 (meters) has entries 1, 1, 2, 1, 3. The fourth column labeled Gravitational Force Objects 1 and 2 (Newtons) has entries 1 G, 2 G, 1 G, 9 G, 3G. Which conclusion is supported by the data in the table? An increase in the mass of an object causes the same decrease in the gravitational force. An increase in the distance between the objects causes the same decrease in the gravitational force. An increase in the distance between the objects causes a greater change in the gravitational force than the same increase in mass. An increase in the mass causes a greater change in the gravitational force than the same increase in the distance between the objects. Brainlyest for correct answer!
Answer:
C
Explanation:
edge 2020... Using elimination it's the only one that makes sense.
The statement third "an increase in the distance between the objects causes a greater change in the gravitational force than the same increase in mass" is correct.
What is gravitational force?The gravitational force is a force that attracts all mass-bearing objects. The gravitational force is referred to as attractive because it always strives to pull masses together rather than pushing them apart.
As we know, the gravitational force is given by:
[tex]\rm F = \dfrac{Gm_1m_2}{r^2}[/tex]
Where, G is the gravitational constant.
m1 and m2 are masses.
r is the distance between the masses.
From the data given in the table, shows that:
The gravitational force is indirectly proportional to the square of the distance.
Thus, the statement third "an increase in the distance between the objects causes a greater change in the gravitational force than the same increase in mass" is correct.
Learn more about the gravitational force here:
https://brainly.com/question/12528243
#SPJ2
Gold-198 is a radioactive isotope, and it has a half-life of about 2.5 days.
You have 100 grams of Gold-198. How many grams remain after 20 days?
3.125 grams
1.5625 grams
0.78125 grams
0.390625 grams
Answer: 0.390625 grams
Explanation:
A half-life of an element is the amount of time that it takes for half the mass of the element to decay.
Gold-198 having a half-life of 2.5 days therefore means that every 2.5 days, the mass is cut in half.
If there are 20 days, find out how many half-life periods there are:
= 20 / 2.5
= 8 periods
The half life is:
= Original mass * 0.5^number of half-life periods
= 100 * 0.5⁸
= 0.390625 grams
A heater has resistance of 10 ohms. It operates at 120 volts. a. What is the current through the heater?
Answer:
I = 12 A
Explanation:
For this exercise we use the relationship that voltage is proportional to the product of current and resistance
V = I R
I = V / R
let's calculate
I = 120/10
I = 12 A
The lens labelled (B) has radius 16.5cm on the curved side. Using the shape of the lens to assign the sign of the radius, calculate the focal length of the lens. Give your answer with the correct positive or negative sign using the usual convention for lenses.
Answer:
convex f = 33 cm
concave f = -33 cm
Explanation:
In geometric optics the focal length of a lens is given by
[tex]\frac{1}{f} = ( n-1) \ (\frac{1}{R_2} - \frac{1}{R_1} )[/tex]
where n is the refractive index of the medium, R₁ and R₂ are the focal lengths on each side of the lens.
In this case one of the sides is flat so its focal length is infinite, if the lens is convex the focal length is positive, convergent lens and if it is concave the focal length is negative, divergent lens.
[tex]\frac{1}{f} = (n-1) \ \frac{1}{R}[/tex]
the refractive index of the glass is n = 1.5
let's calculate
1 / f = (1.5 -1) 1 / 16.5
1 / f = 0.03030
f = 33 cm
convex f = 33 cm
concave f = -33 cm
In any given wave, when the frequency of the wave doubles (f = 2f), which of the following other changes would also take place?
A The wavelength would double (λ = 2λ).
B The velocity would double (v = 2v).
C The wavelength would be half (λ = λ/2).
D The velocity would be half (v = v/2).
Answer:
The correct answer is -
B. The velocity would double (v = 2v).
C. The wavelength would be half (λ = λ/2).
Explanation:
A wave has a speed or velocity that is related to the wavelength of the wave and the frequency of the wave and this relationship can be represented by the following equation-
Wave velocity V = Wavelength (λ) * Frequency (f)
Frequency (f) = Velocity (V) / Wavelength(λ).
The frequency and wavelength are inversely proportional and frequency and velocity are directly proportional to each other.
So, if f = 2f then,
putting value in the formula,
2f = 2v/λ, which means, f = 2v and f = λ/2
when the frequency is doubled, the wavelength will be halved and velocity will be doubled.
A metal with work function 1.17 eV is illuminated with light of wavelength 437 nm. What stopping potential is required for the photoelectrons
Answer: [tex]1.67\ V[/tex]
Explanation:
Given
Work function [tex]\phi =1.17\ eV[/tex]
The wavelength of the light is [tex]\lambda =437\ nm[/tex]
Energy associated with this wavelength is
[tex]E=\dfrac{hc}{\lambda}\\\\\Rightarrow E=\dfrac{1.99\times 10^{-25}}{437\times 10^{-9}}\\\\\Rightarrow E=4.553\times 10^{-19}\ J\\\\\Rightarrow E=2.841\ eV[/tex]
Stopping potential is
[tex]V=\dfrac{E-\phi }{e}\\\\\Rightarrow V=\dfrac{\left(2.841-1.17\right)e}{e}\\\\\Rightarrow V=1.67\ V[/tex]
What is an electron?
(it’s D lol)
Answer:
D
Explanation:
A 400 kg satellite is in a circular orbit at an altitude of 500 km above the Earth's surface. Because of air friction, the satellite eventually falls to the Earth's surface, where it hits the ground with a speed of 1.60 km/s. How much energy was transformed into internal energy by means of air friction
Answer:
E = 1.45 x 10⁹ J = 1.45 GJ
Explanation:
According to the law of conservation of energy:
Potential Energy Lost by Satellite = Kinetic Energy + Internal Energy
[tex]mgh = \frac{1}{2} mv^2 + E\\\\E = mgh - \frac{1}{2} mv^2[/tex]
where,
E = Internal Energy = ?
m = mass = 400 kg
g = acceleration due to gravity = 9.81 m/s²
h = height = 500 km = 500000 m
v = speed on ground = 1.6 km/s = 1600 m/s
Therefore,
[tex]E = (400\ kg)(9.81\ m/s^2)(500000\ m)-\frac{1}{2} (400\ kg)(1600\ m/s)^2\\E = 1.962\ x\ 10^9\ J - 0.512\ x\ 10^9\ J[/tex]
E = 1.45 x 10⁹ J = 1.45 GJ
Which of the following is NOT a reason why humans sleep?
Sleep helps to restore and repair brain tissue.
Sleep restores and rebuilds memories.
Sleep provides a psychic safety valve to discharge unacceptable feelings.
During sleep, growth hormone is released, especially in children.
Answer and Explanation:
The answer is the second answer choice. This is because we humans can rebuild or build memories during the day, it doesn't have to happen via sleep.
The first answer choice IS a reason because you aren't working your brain as hard, so your brain has time to heal. A mouse study suggests that sleep helps restore the brain by flushing out toxins that build up during waking hours.
The third answer choice IS a reason because of the idea of Wish Fulfillment: Sigmund Freud suggested that dreams provide a psychic safety valve to discharge unacceptable feelings. The dream's manifest (apparent) content may also have symbolic meanings (latent content) that signify our unacceptable feelings.
The forth answer choice IS a reason because of the idea of Cognitive Development: Some researchers argue that we dream as a part of brain maturation and cognitive development.
#teamtrees #PAW (Plant And Water)
A current 2a flows in a circuit fir 2 minutes. Calculate the charge generated in a circuit
Answer:
the charge generated in the circuit is 240 C.
Explanation:
Given;
current flowing in the circuit, I = 2A
time of current flow, t = 2 minutes = 2 x 60s = 120 s
The current flowing through a given circuit is defined as the quantity of charge flowing through the circuit in a given time.
[tex]I = \frac{Q}{t} \\\\Q = I t[/tex]
where;
Q is the charge flowing in the circuit
Q = 2 x 120
Q = 240 C
Therefore, the charge generated in the circuit is 240 C.
two spheres of radii 5cm and 3cm are given charges on risk volume and 50 calling respectively and then connected by a wire calculate the loss of energy after connection
Answer:
Solution given:
Radius of small sphere[r]=5cm=0.05m
Radius of large sphere[R]=10cm=0.1m
capacitance of small sphere[c]=4πε0r
=[tex]4π*8.85×10^{-12}×0.05=5.56*10^{-12}F[/tex]
Charge for small sphere[Q1]=100C
Charge for small sphere[Q2]=50C
Potential difference [V1]=[tex] \frac{charge}{capacitance}=\frac{100}{5.56*10^{-12}}=1.8×10^{13}[/tex]V
.
again
capacitance of small sphere[C]=4πε0R
=[tex]4π*8.85×10^{-12}×0.1=1.11*10^{-11}F[/tex]
Potential difference [V2]=[tex] \frac{charge}{capacitance}=\frac{50}{1.11*10^{-11}}=4.5×10^{12}[/tex]V
Now
Loss of energy:
[tex] \frac{cC(V1-V2)^{2}}{2(c+C)}[/tex]
=[tex] \frac{5.56*10^{-12}*1.11*10^{-11}(1.8*10^{13}-4.5*10^{12})^{2}}{2(5.56*10^{-12}+1.11*10^{-11})}[/tex]
=25Joule
What is the typical pH of acid rain?
Answer:
5.0-5.5 is the answer to your question
Besides ethical considerations, what is another reason why Milgram’s experiment may be difficult to duplicate?
The amount of change between the crest or trough of a wave and the normal