Wave Phenomena (DP IB Physics)

Reflection is when a wave hits a boundary between two media and bounces back to the original medium without passing through.

The law of reflection states that the angle of incidence, , equals the angle of reflection, .

False.

During reflection, the frequency, wavelength, and speed of the wave do not change.

Refraction is the change in direction of a wave when it passes through a boundary between mediums of different densities.

When a wave travels from a less dense medium to a more dense medium, its speed decreases.

The angle of incidence is the angle between the incident ray and the normal line at the boundary between two media.

When light travels from air to glass, its speed decreases, its wavelength decreases, and it refracts towards the normal.

False.

Refraction always involves the transmission of the wave into the second medium.

Transmission is when a wave passes through a substance, and refraction is a specific type of transmission involving a change in direction.

When light travels from a denser to a less dense medium, the angle of refraction is greater than the angle of incidence, causing the light to bend away from the normal.

The wave behaviour shown in the daigram is reflection.

Refraction does not take place when the light ray passes from air into the glass block in the diagram because the ray has an angle of incidence of zero, it is incident along the normal line.

The wave phenomenon shown in the diagram is diffraction.

Diffraction is the spreading out of waves after they pass through a narrow gap or around an obstruction.

True.

Diffraction occurs when waves pass through an aperture or around a barrier.

Wave amplitude decreases during diffraction through an aperture because the barrier on either side of the gap absorbs wave energy.

Gap size relative to wavelength affects diffraction because diffraction occurs when the gap size is similar to the wavelength. More diffraction occurs if the wavelength is larger than the gap size.

When waves pass through a gap much larger than the wavelength, the majority of the wave passes straight through with little diffraction.

Diffraction around a barrier is when waves curve around the edge of the barrier and spread out behind it.

The extent of diffraction around a barrier is determined by the wavelength of the waves. Longer wavelengths undergo greater diffraction.

The effect of a barrier larger than the wavelength is some diffraction occurs and a shadow region forms behind the barrier where no wavefronts are present.

Wavelength compared to barrier size affects diffraction because if the barrier is the same size as the wavelength, there is more diffraction and a smaller shadow region behind the barrier.

Optimal diffraction occurs when the wavelength is comparable to the size of the gap or barrier.

Snell's law relates the angle of incidence to the angle of refraction at a boundary between two media.

The refractive index, , of a material tells us how optically dense it is.

True.

The refractive index of air is = 1.

The refractive index of a material is calculated using the equation .

Where:

• = absolute refractive index of the medium

• = speed of light in a vacuum, measured in metres per second (ms^-1)

• = speed of light in the medium, measured in metres per second (ms^-1)

The critical angle is the angle of incidence at which the angle of refraction is 90°, causing the light to travel along the boundary between media.

Total internal reflection occurs when the angle of incidence within the denser medium is greater than the critical angle.

Snell's law is expressed as:

Where:

• = refractive index of medium 1

• = refractive index of medium 2

• = angle of incidence in medium 1, measured in degrees ()

• = angle of refraction in medium 2, measured in degrees ()

The two conditions for total internal reflection to occur are:

• the refractive index of medium 1 < refractive index of medium 2 ( )

• angle of incidence > critical angle ()

The equation for the critical angle, , is found using the equation:

Where:

• = refractive index of medium 2

• = refractive index of medium 1

The higher the refractive index of a material, the more optically dense it is, and the slower light will travel through it.

Superposition is when two or more waves arrive at the same point and their amplitudes combine.

The principle of superposition states that when two or more waves overlap at a point, the displacement at that point is the sum of the displacements of the individual waves.

False.

The principle of superposition applies to both transverse and longitudinal waves.

Constructive interference occurs when two or more waves superimpose and have displacements in the same direction.

Destructive interference occurs when two or more waves superimpose and have displacements in opposite directions.

Waves interfere constructively when they are in phase and their displacements add together to form a larger displacement.

After waves undergo superposition, they continue to travel as normal.

Resultant displacement is the vector sum of the displacements of individual waves when they overlap.

For a clear interference pattern, the waves must be of the same type, amplitude, frequency, and have a constant phase difference.

The amplitude of the resultant waves in the diagram is the sum of the amplitude of the two individual waves because the two waves are superposed.

The path difference between the waves coming from S₁ and S₂ in the diagram is 2.

Double-source interference involves producing a diffraction and interference pattern using either two coherent wave sources or a single wave source passing through a double slit.

Double-source interference can be observed using the following wave sources:

• A laser beam

• Two speakers emitting coherent sound

• Microwaves diffracted through two slits

Interference is the effect observed due to the superposition of two or more waves.

Constructive interference occurs when two waves meet in phase, resulting in the waves adding together.

Destructive interference occurs when two waves meet in antiphase, resulting in the waves cancelling each other out.

True.

Coherent waves have the same frequency and a constant phase difference.

Path difference is the difference in the distance travelled by two waves from their sources to the point at which they meet.

The condition for constructive interference is path difference = , where is an integer.

The condition for destructive interference is path difference , where is an integer.

On a wavefront diagram, interference is determined by counting the number of wavelengths to determine if constructive or destructive interference occurs at a point.

The features of a diffraction pattern that indicate a double-slit diffraction pattern are:

• each bright fringe is identical in width and intensity

• the fringe spacing is equal

Double-source interference involves producing a diffraction and interference pattern using either two coherent wave sources or a single wave source passing through a double slit.

True.

Coherent waves have the same frequency and a constant phase difference.

The nature of interference is determined using a wavefront diagram by counting the number of wavelengths between the two wave sources to see if it is constructive or destructive at a point.

Monochromatic waves have the same wavelength, so for visible light, they are the same colour.

The equipment required in Young's double slit experiment is:

• a monochromatic light source

• a single slit

• a double slit

• a screen

The type of diffraction observed on the screen shown in the diagram is double-slit diffraction.

A single slit diffraction pattern is a series of light and dark fringes produced by monochromatic light passing through a single rectangular slit onto a screen.

The central maximum is the brightest and widest fringe in a single slit diffraction pattern.

True.

The central maximum in a single-slit diffraction pattern is wider than the maxima in a double-slit diffraction pattern.

Increasing the wavelength of the incident light increases the angle of diffraction, causing wider fringes.

The relationship between slit width and the angle of diffraction in a single slit diffraction pattern is inversely proportional to the slit width.

The equation for the angle of diffraction in terms of slit width is

Where:

• is the angle of diffraction, measured in degrees ()

• is the wavelength of the incident light, measured in metres (m)

• is the single slit width, measured in metres (m)

Dark fringes of destructive interference in single slit diffraction patterns:

• are narrower than the bright fringes

• are less bright than the bright fringes

• get dimmer further from the central maxima

The effect of narrowing the slit width in a single slit diffraction pattern is that it increases the angle of diffraction, creating wider fringes that are less intense.

Increasing the distance between the slit and the screen in a single slit diffraction experiment increases the width of the fringes.

A fringe is a bright or dark band resulting from the constructive or destructive interference of light waves.

A diffraction grating is a piece of optical equipment with many parallel slits that diffract light to produce a diffraction pattern.

True.

Increasing the number of slits in a diffraction grating increases the intensity of the maxima.

In the diffraction grating equation, represents the distance between the slits.

The diffraction grating equation is

Where:

• n = the order of maxima

• = wavelength of incident light, measured in metres (m)

• = slit separation, measured in metres (m)

• = angle of diffraction, measured in degrees ()

Angular separation is the angle between two maxima in a diffraction pattern.

The diffraction pattern obtained when white light is incident in a diffraction grating is different wavelengths of light separated into spectra.

Decreasing the slit spacing increases the angle of diffraction, creating wider fringes.

The shortest wavelength, violet/blue, appears closest to the central maximum in a diffraction pattern of white light.

The order of maxima is the number representing the position of a bright fringe from the central maximum.

The trigonometric relationship between the wavelength, , slit separation, , and angle of diffraction, , as shown in the diagram is: