Physics Chapter on Microscope and Electric Fields

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Questions and Answers

What does Snell's law relate in the context provided?

The refractive indices and angles of incidence and refraction (correct)

The types of media based on their densities

The speed of light in different mediums

The nature of light as a wave and a particle

In triangle AOC, how is the angle 'i' expressed?

i = 2α + γ

i = β + γ

i = α + γ (correct)

i = α + β + γ

What results from the substitution of angles in the equation involving refractive indices?

μ1/i = μ2/r

μ1 tan α = μ2 tan r

μ1 + μ2 = μ2 - μ1 (correct)

μ1 + μ2 = μ1(PC/PI) - μ2(PO/PC)

What do the linear relationships in the equations imply about angles α, β, and γ?

They can be approximated by their sine values Signup and view all the answers

Which relationship is derived from the equations provided from the context?

μ1/PO + μ2/PI = (μ2 - μ1)/PC Signup and view all the answers

What is the principle behind the linear magnification of a concave spherical mirror?

The focal length of the mirror Signup and view all the answers

Which equation is used to determine the magnifying power of a simple microscope when the image is formed at D?

$M = 1 + \frac{D}{f}$ Signup and view all the answers

In which scenario is the magnifying power of a compound microscope calculated for an image formed at infinity?

When the ocular lens acts as a magnifier Signup and view all the answers

What does the laws of refraction based on wave theory primarily focus on?

The speed of light in various mediums Signup and view all the answers

What does Bohr's theory of the hydrogen atom primarily describe?

The behavior of electrons in quantum states Signup and view all the answers

What condition is necessary for constructive interference to occur?

Phase difference is a multiple of $2\pi$ Signup and view all the answers

What does the concept of nuclear density relate to?

The mass per unit volume of atomic nuclei Signup and view all the answers

What role does the electric field play in the context of an electric dipole?

It is the resultant of individual fields generated by both charges Signup and view all the answers

What is the formula for magnifying power when the image is formed at the least distance of distinct vision?

M = 1 + $\frac{D}{f}$ Signup and view all the answers

What is the significance of using a convex lens with a short focal length in a magnifying glass?

It magnifies small objects effectively. Signup and view all the answers

When the first clear image is seen at D, what relationship do u, D, and f share according to the content?

u = D - f Signup and view all the answers

Which of the following determines the magnifying power at infinity for a simple microscope?

The ratio $\frac{D}{f}$ Signup and view all the answers

In what scenario are the angles α and β replaced by their tangents when discussing magnifying power?

When they are small angles Signup and view all the answers

Which equation represents the relationship between u, D, and f in the context of magnifying power?

$\frac{1}{f} = \frac{1}{u} - \frac{1}{D}$ Signup and view all the answers

What is the practical implication of the statement 'the first clear image is always seen at D'?

Objects must be placed at D for magnification. Signup and view all the answers

Which parameter is critical when calculating the magnifying power of a simple microscope?

Focal length of the lens Signup and view all the answers

What is the relationship between tan α and the distances AN and NO?

tan α = AN / NO Signup and view all the answers

Which equation correctly represents the relationship between the refractive indices and the distances for the lens?

μ1 + μ2 = (μ2 - μ1) / (P1O + P1C1) Signup and view all the answers

According to the content, what represents the radius of curvature in the equations derived?

R Signup and view all the answers

What is the significance of P1 in the context of the lens with refracting surface?

P1 is a point object located on the principal axis. Signup and view all the answers

What can be inferred about the angles i and r1 in the prism described?

i and r1 represent corresponding angles in the prism Signup and view all the answers

What does the term 'angle of deviation' refer to in the context of the prism?

The total shift in the path of the light ray Signup and view all the answers

What is the value of r in relation to γ and β as stated in the equations?

r = γ - β Signup and view all the answers

Which equation represents the relationship derived from the triangles ANO and ANC?

i = tan α + tan γ Signup and view all the answers

What is the formula for the distance of closest approach (r0) for a hydrogen-like atom?

$r_0 = \frac{4\pi \epsilon_0 \cdot nh^2}{4\pi^2 m e^2}$ Signup and view all the answers

What is the approximate size of a nucleus derived from the Geiger-Marsden experiment?

$4 \cdot 13 \times 10^{-14} m$ Signup and view all the answers

Which equation expresses the energy of an electron in the nth orbit of a hydrogen-like atom?

$E_n = -\frac{Z^2 me^4}{4\pi\epsilon_0 n^2 h^2}$ Signup and view all the answers

In Bohr's theory of hydrogen atom, what type of orbit does the electron follow?

Circular orbit Signup and view all the answers

What is the kinetic energy (Ek) of the electron in the nth orbit represented by?

$E_k = \frac{1}{2} mv^2$ Signup and view all the answers

What aspect does the parameter Z represent in the formulas concerning hydrogen-like atoms?

Atomic number of the atom Signup and view all the answers

Which expression gives the velocity (v) of an electron in the nth orbit?

$v = \frac{nh}{2\pi m 4\pi \epsilon_0}$ Signup and view all the answers

What is the main principle behind the Geiger-Marsden experiment?

To estimate the size of the nucleus Signup and view all the answers

Study Notes

Simple Microscope (Magnifying Glass)

A convex lens with short focal length enables magnification of small objects.
Magnifying power (M) of a simple microscope relates object distance (u) and least distance of distinct vision (D).
For an image formed at D:
- Magnifying power can be formulated as M = D/u.
When the object is at the least distance of distinct vision (25 cm), the angle subtended by the image (β) and object (α) at the eye can be used to define magnification.
The relationship between angles is captured in the equation: M = β/α.
For small angles, magnifying power can also be simplified to M ≈ D/f, where f is the focal length of the lens.
The formula adapts for different scenarios, including when the image is formed at infinity.

Electric Field and Charges

Consider an electric dipole with charges -q and +q, separated by distance 2a.
Resultant electric field at point P due to dipole is the sum of electric fields from both charges.
When considering refraction:
- Apply Snell’s law: μ₁ sin i = μ₂ sin r, correlating angles in different media.
Using new Cartesian sign conventions, object distance (u), image distance (v), and radius of curvature (R) are defined positively and negatively depending on their positions.

Lens Maker's Formula

Refers to how a lens with refractive index μ₁ interacts with surrounding media of refractive index μ₂.
The relationship involving distances before and after refraction can be expressed as:
- μ₁/PO + μ₂/P1I1 = (μ₂ - μ₁)/P1C1.
Thin lens approximation allows simplification of distances close to the optical center.

Bohr's Theory of Hydrogen Atom

Describes an electron in a hydrogen atom revolving around a nucleus.
Energy of the electron in the nth orbit is derived using:
- En = - (2π²Z²me⁴)/(4πε₀n²h²), where Z is atomic number.
The kinetic energy (Ek) of the electron within its orbit follows the relationship:
- Ek = mv²/2, indicating a connection between mass, velocity, and energy.
Experimentally determined size of the nucleus finds r₀ ≈ 4.13 × 10⁻¹⁴ m, indicating the nucleus is on the order of 10⁻¹⁴ m.

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Description

Explore the fundamentals of simple microscopes and electric fields in this quiz. Understand the concepts of magnifying power using lenses and the behavior of electric dipoles. Test your knowledge on related equations and principles.