Презентация к уроку на тему " Huygens principle and refraction"

What types of spherical mirrors do you know?

What can you tell us about the focal length of a convex mirror?

What is the physical meaning of the focal length minus?

How is the radius of curvature of the lens and the focal length related?

Specify the formula for a spherical mirror?

Refraction

Refraction is the bending of light as it passes from one medium into another.

Note: the angle of incidence qA in air and the angle of refraction qA in water are each measured with the normal N.

The incident and refracted rays lie in the same plane and are reversible.

Refraction Distorts Vision

The eye, believing that light travels in straight lines, sees objects closer to the surface due to refraction. Such distortions are common.

The Index of Refraction

The index of refraction for a material is the ratio of the velocity of light in a vacuum (3 x 108 m/s) to the velocity through the material.

Examples: Air n= 1; glass n = 1.5; Water n = 1.33

Example 1. Light travels from air (n = 1) into glass, where its velocity reduces to only 2 x 108 m/s.What is the index of refraction for glass?

If the medium were water: nW = 1.33. Then you should show that the velocity in water would be reduced from c to 2.26 x 108 m/s.

Analogy for Refraction

Light bends into glass then returns along original path much as a rolling axle would when encountering a strip of mud.

3 x 108 m/s

3 x 108 m/s

2 x 108 m/s

Deriving Snell’s Law

Consider two light rays. Velocities are v1 in medium 1 and v2 in med. 2.

Segment R is common hypotenuse to two rgt. triangles. Verify shown angles from geometry.

Snell’s Law

The ratio of the sine of the angle of incidence q1 to the sine of the angle of refraction q2 is equal to the ratio of the incident velocity v1 to the refracted velocity v2 .

Example 2: A laser beam in a darkened room strikes the surface of water at an angle of 300. The velocity in water is 2.26 x 108 m/s. What is the angle of refraction?

The incident angle is:

qA = 900 – 300 = 600

qW = 35.30

qA

Snell’s Law and Refractive Index

Another form of Snell’s law can be derived from the definition of the index of refraction:

Snell’s law for velocities and indices:

A Simplified Form of the Law

Since the indices of refraction for many common substances are usually available, Snell’s law is often written in the following manner:

The product of the index of refraction and the sine of the angle is the same in the refracted medium as for the incident medium.

Example 3. Light travels through a block of glass, then remerges into air. Find angle of emergence for given information.

First find qG inside glass:

qG = 30.70

From geometry, note angle qG same for next interface.

qG

Wavelength and Refraction

The energy of light is determined by the frequency of the EM waves, which remains constant as light passes into and out of a medium. (Recall v = fl.)

lG < lA

The Many Forms of Snell’s Law:

Refraction is affected by the index of refraction, the velocity, and the wavelength. In general:

All the ratios are equal. It is helpful to recognize that only the index n differs in the ratio order.

Example 4: A helium neon laser emits a beam of wavelength 632 nm in air (nA = 1). What is the wavelength inside a slab of glass (nG = 1.5)?

nG = 1.5; lA = 632 nm

Note that the light, if seen inside the glass, would be blue. Of course it still appears red because it returns to air before striking the eye.

Points A and B are the sources of spherical wavelets.
Then BC = υ1t ; AD = υ2t.
Referring to Δ ABC and Δ ADC, we see that
𝒔𝒔𝒊𝒊𝒏𝒏𝒊𝒊= 𝑩𝑪 𝑨𝑪 𝑩𝑩𝑪𝑪 𝑩𝑪 𝑨𝑪 𝑨𝑨𝑪𝑪 𝑩𝑪 𝑨𝑪 and 𝒔𝒔𝒊𝒊𝒏𝒏𝒓𝒓= 𝑨𝑫 𝑨𝑪 𝑨𝑨𝑫𝑫 𝑨𝑫 𝑨𝑪 𝑨𝑨𝑪𝑪 𝑨𝑫 𝑨𝑪
𝒔𝒊𝒏𝒊 𝒔𝒊𝒏𝒓 𝒔𝒔𝒊𝒊𝒏𝒏𝒊𝒊 𝒔𝒊𝒏𝒊 𝒔𝒊𝒏𝒓 𝒔𝒔𝒊𝒊𝒏𝒏𝒓𝒓 𝒔𝒊𝒏𝒊 𝒔𝒊𝒏𝒓 = 𝑩𝑪 𝑨𝑫 𝑩𝑩𝑪𝑪 𝑩𝑪 𝑨𝑫 𝑨𝑨𝑫𝑫 𝑩𝑪 𝑨𝑫 = 𝝊 𝟏 𝒕 𝝊 𝟐 𝒕 𝝊 𝟏 𝝊𝝊 𝝊 𝟏 𝟏𝟏 𝝊 𝟏 𝒕𝒕 𝝊 𝟏 𝒕 𝝊 𝟐 𝒕 𝝊 𝟐 𝝊𝝊 𝝊 𝟐 𝟐𝟐 𝝊 𝟐 𝒕𝒕 𝝊 𝟏 𝒕 𝝊 𝟐 𝒕 = 𝝊 𝟏 𝝊 𝟐 𝝊 𝟏 𝝊𝝊 𝝊 𝟏 𝟏𝟏 𝝊 𝟏 𝝊 𝟏 𝝊 𝟐 𝝊 𝟐 𝝊𝝊 𝝊 𝟐 𝟐𝟐 𝝊 𝟐 𝝊 𝟏 𝝊 𝟐 = 𝒏 𝟐 𝒏 𝟏 𝒏 𝟐 𝒏𝒏 𝒏 𝟐 𝟐𝟐 𝒏 𝟐 𝒏 𝟐 𝒏 𝟏 𝒏 𝟏 𝒏𝒏 𝒏 𝟏 𝟏𝟏 𝒏 𝟏 𝒏 𝟐 𝒏 𝟏

Total Internal Reflection

The critical angle qc is the limiting angle of incidence in a denser medium that results in an angle of refraction equal to 900.

When light passes at an angle from a medium of higher index to one of lower index, the emerging ray bends away from the normal.

When the angle reaches a certain maximum, it will be reflected internally.

Example 5. Find the critical angle of incidence from water to air.

For critical angle, qA = 900

nA = 1.0; nW = 1.33

In general, for media where n1 > n2 we find that:

Dispersion by a Prism

Dispersion is the separation of white light into its various spectral components. The colors are refracted at different angles due to the different indexes of refraction.

Dispersion is the dependence of the index of refraction upon the wavelength or frequency of light. Usually, the index of refraction is lower for longer wavelengths.

For example, the refractive index of glass for red light is less than that for blue light, due to this, blue light refracts more than red light does.

PROBLEM: Light is incident on an equilateral glass prism at a 45.0° angle to one face (Figure below). Calculate the angle at which light emerges from the opposite face.

Light through a Parallel Sided Transparent Medium

PROBLEM:
Determine the linear displacement of the beam as it passes through a plane-parallel glass plate with a refractive index n2 = 1.7, thickness d = 4 cm. The angle of incidence of the beam is 30 °. The refractive index of air is n =1.