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Alinara [238K]
4 years ago
6

Using Rayleigh's criterion, what is the smallest separation between two pointlike objects that a person could clearly resolve at

his near point of 20.5 cm with a pupil diameter of 2.15 mm ? Assume that the light has a wavelength of 550 nm . (To get a reasonable estimate without having to go through complicated calculations, we'll ignore the effect of the fluid in the eye.)
Physics
1 answer:
atroni [7]4 years ago
7 0

 Answer:

y = 52.44 10⁻⁶  m

Explanation:

It is Rayleigh's principle that two points are resolved if the maximum of the diffraction pattern of one matches the minimum the diffraction pattern of the other

Based on this principle we must find the angle of the first minimum of the diffraction expression

         a sin θ= m λ

The first minimum occurs for m = 1

       sin θ =  λ  / a

Now let's use trigonometry the object is a distance L = 0.205 m

        tan θ = y / L

Since the angles are very small, let's approximate

        tan θ = sin θ/cos θ = sin  θ

        sin θ = y / L

We substitute in the diffraction equation

         y / L =  λ  / a

         y =  λ  L / a

Let's calculate

        y = 550 10⁻⁹ 0.205 / 2.15 10⁻³

        y = 52.44 10⁻⁶ m

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atoms are composed of several basic types of very small ____; the ____ of each of these particles gives a different kinds of ato
Lesechka [4]

Answer:

An atom is the smallest unit of matter that retains all of the chemical properties of an element. Atoms combine to form molecules, which then interact to form solids, gases, or liquids. For example, water is composed of hydrogen and oxygen atoms that have combined to form water molecules. Many biological processes are devoted to breaking down molecules into their component atoms so they can be reassembled into a more useful molecule.

Atomic Particles

Atoms consist of three basic particles: protons, electrons, and neutrons. The nucleus (center) of the atom contains the protons (positively charged) and the neutrons (no charge). The outermost regions of the atom are called electron shells and contain the electrons (negatively charged). Atoms have different properties based on the arrangement and number of their basic particles.

The hydrogen atom (H) contains only one proton, one electron, and no neutrons. This can be determined using the atomic number and the mass number of the element (see the concept on atomic numbers and mass numbers).

4 0
3 years ago
Read 2 more answers
A square plate of copper with 47.0 cm sides has no net charge and is placed ina region of uniform electric field of 75.0 kN/C di
timurjin [86]

Answer:

(a) Charge density σ=6.6375×10²nC/m²

(b) Total charge Q=1.47×10²nC

Explanation:

Given Data

A=47.0 cm =0.47 m

Electric field E=75.0 kN/C

To find

(a) Charge density σ

(b)Total Charge Q

Solution

For (a) charge density σ

From Gauss Law we know that

Φ=Q/ε₀.......eq(i)

Where

Φ is electric flux

Q is charge

ε₀ is permittivity of space

And from the definition of flux

Φ = EA

The flux is  electric field passing  perpendicularly through the surface

Put the this Φ in equation(i)

EA =Q/ε₀

where Q(charge)=σA

EA=(σA)/ε₀

E=σ/ε₀

σ=ε₀E

=(8.85*10^{-12} )*(75.0*10^{3} )\\=6.6375*10^{-7} C/m^{2}\\=6.63*10^{2}nC/m^{2}

σ=6.6375×10²nC/m²

For (b) total charge Q

Q=σA

Q=(6.6375*10^{2} nC/m^{2} )(0.47m)^{2}\\ Q=1.47**10^{2}nC

6 0
3 years ago
(I) A novice skier, starting from rest, slides down an icy frictionless 8.0° incline whose vertical height is 105 m. How fast is
Vlad1618 [11]

Answer:

v = 45.37 m/s

Explanation:

Given,

angle of inclination = 8.0°

Vertical height, H  = 105 m

Initial K.E. = 0 J

Initial P.E. = m g H

Final PE = 0 J

Final KE = \dfrac{1}{2}mv^2

Using Conservation of energy

KE_i + PE_i + KE_f + PE_f

0 + m g H = \dfrac{1}{2}mv^2 + 0

v = \sqrt{2gH}

v = \sqrt{2\times 9.8 \times 105}

v = 45.37 m/s

Hence, speed of the skier at the bottom is equal to v = 45.37 m/s

3 0
3 years ago
If a machine has an efficiency of 50% and an input of 3 J, what is the output?
uranmaximum [27]

Answer:

150J

Explanation:

work output/work input=100%

so just make work output the subject

6 0
3 years ago
Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject materia
melisa1 [442]

Answer:

H_2 = 91.55 km

Explanation:

Gravity on the surface of planet is given as

g = \frac{GM}{R^2}

as we know that

M = 8.93 \times 10^{22} kg

R = 1821 km

now gravity on the planet is

g = \frac{(6.67 \times 10^{-11})(8.93 \times 10^{22})}{(1821 \times 10^3)^}

so we have

g = 1.8 m/s^2

now we know that

H_{max} = \frac{v^2}{2g}

so we will say

\frac{H_1}{H_2} = \frac{g_2}{g_1}

\frac{500}{H_2} = \frac{9.81}{1.8}

H_2 = 91.55 km

5 0
3 years ago
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