Light makes up a small part of the entire spectrum of waves, which can include radio waves, microwaves, and rays of the sun.
Most waves require a material medium for their transmission, but can travel through empty space.
The direction of propagation of the wave is determined by the electric and magnetic fields that are oscillated to each other.
Like all the waves, we can say v.
If we oscillate one end of a long rope, we can generate a wave that travels down the rope and has the same frequencies as the oscillation.
In a similar way, you can think of anEM wave, which is composed of magnetic and electric fields, when you think of an electric charge.
The wave was created by the electric charge that created these fields.
The fields are parallel to each other and the direction of propagation.
For this reason, the waves are not straight.
The direction of the wave's electric field is called the polarization of the wave.
Unlike waves on a rope or sound waves, electromagnetic waves do not require a material medium to propagation; they can travel through empty space.
The speed of the wave is constant at 3 x 10 8 m/s.
The full range of waves is called the EM spectrum and can be categorized by their wavelength.
There is no universal agreement on the boundaries of the different types of waves.
You should be familiar with the names of the major categories and the order of the colors within the visible spectrum.
The colors red, orange, yellow, green, blue, and violet are used to increase wave frequencies.
The visible spectrum of colors are expressed in nanometers.
Yellow light can be seen when the wave's wavelength is between 577 and 597 nm.
The waves travel through a vacuum at this speed.
The most important equation for waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves and waves The equation becomes l f + c when the waves travel through a vacuum.
According to the spectrum presented above, the waves with 10 -2 m are microwaves.
Waves experience interference when they meet, and whether they interfere negatively or positively depends on their relative phase.
They combine destructively if they meet out of phase.
This observation is the key to the interference patterns we'll study in the next section.
If waves with the same wavelength meet, the difference in the distances they've traveled will determine whether the waves are in phase.
They'll arrive exactly out of phase if this difference is a whole number plus one-half a wavelength.
There is a light incident on a barrier that has two narrow slits separated by a distance.
The screen on the right is larger than the barrier.
You might think that we'll only see two bright narrow strips of light, directly opposite of the barrier.
It doesn't take into account the wave nature of light.
After a wave passes through a width similar to its wavelength, it will fan out.
Diffraction is the change in the propagation of a wave when it encounters a barrier.
Waves will spread out and interfere with the screen in the set-up above.
There are points of interference in the figure above.
Solid lines intersecting each other are points of constructive interference.
Solid lines intersecting dashed lines are points of destructive interference.
The screen will show the results of the interference, with bright bands and dark fringes at the points where the waves interfere.
The locations of the fringes should be determined.
We labeled the slit S 1 and S 2.
A point P on the screen is selected, the path lengths from S 1 and S 2 to P are called l 1 and l 2 respectively, and the angle that the line from the middle of the slit to P makes with the horizontal is th.
To find the bright fringes on the screen, we use the fact that x is L.
As m increases in magnitude, the intensity of the bright fringes decreases.
The central maximum will have the greatest intensity when m is 0.
The bright fringes with m 1 will have a lower intensity than the ones with m 2.
The interference pattern becomes sharper if more than two slits are cut in the barrier.
Barriers containing thousands of tiny slit per centimeter are used for this purpose.
If d is 1.5mm, L is 6.0 m, and the light wavelength is 589 nm, then we have a set-up.
The first maximum above the central one is labeled x 1.
The other bright fringes are labeled accordingly.
The interference pattern would be spread out, as the fringes would become larger.
If the barrier only has one slit, a pattern will form on the screen.
The central maximum will be very pronounced, but lower-intensity maxima will also be seen because of interference from waves arriving from different locations.
As the width of the slit is decreased, the width of the central maximum will become wider.
There is a central, bright circular disk surrounded by rings of decreasing intensity.
Imagine a beam of light hitting a transparent surface.
Some of its energy will be reflected off the surface and some will be transmitted into a new medium when it hits this surface.
We can figure out the directions of the reflected and transmitted beams by calculating the angles that the beams make with the normal to the interface.
The figure shows a beam of light in the air hitting a piece of glass.
The angles are measured from the normal.
The normal is always on the surface.
When a question asks for the angle of incidence or reflection, it wants the angle formed with the normal, not the angle to the horizontal surface.
You need to know if you're solving for the angle of incidence, angle of reflection, or the angle it forms with the mirror.
The angle of incidence is the angle of the incident beam to the normal.
The angle of reflection is the angle of the reflected beam to the normal and the angle of the transmitted beam to the normal.
There are beams of light in the same plane.
The Law of Reflection states that the angle of reflection is the same as the angle of incidence.
We need to talk about a medium's index of refraction in order to describe how th 1 and th 2 are related.
One of the fundamental constants of nature is the speed at which light travels through empty space.
When light travels through a material medium, it's constantly being absorbed and re-emitted by the atoms that compose the material and, as a result, its apparent speed, v, is some fraction of c.
Light always travels slower in a medium than in a vacuum, so it's never less than 1.
The norm is to consider the index of refraction of air to be 1 because it is so close to 1.
The beam will bend toward the normal as it enters the medium if n 2 > n 1 is true.
If n 2 n 1, then th 2 > th 1, the beam will bend away from the normal.
A beam of light in the air strikes a piece of glass at an angle of 30 degrees.
If the light beam makes an angle of 30 degrees with the surface, then it makes an angle of 60 degrees with the normal.
The angle of reflection is 60 degrees.
Snell's Law is used to find the angle of refraction.
The air's index is close to 1 so we can say that n is 1 for air.
The glass has a greater index than the air, so we would expect that.
A fisherman drops a flashlight into a lake.
The flashlight sinks to the bottom where its light beam is directed almost vertically upward toward the lake's surface, making a small angle with the normal.
The figure is below.
The beam of light will bend away from the normal as it emerges from the water since the air has a lower index than the water.
When we studied waves, we learned that wave speed is not dependent on Frequency.
For a given medium, different frequencies give rise to different wavelengths, because the equation v is always satisfied and v doesn't vary.
dispersion is a variation in wave speed with wavelength when light travels through a material medium.
The definition of the index of refraction should be accompanied by a statement of the frequencies of the light used to measure v.
As the wavelength decreases, the index increases.
Higher frequencies have higher indices of refraction.
The yellow light of wavelength 589 nm is used to calculate most lists of Refractive index values.
When white light hits a glass prism, the beam is split into its component colors and the variation in the values of the Refractive index across the visible spectrum is small.
Snell's Law tells us that each color has its own angle of refraction.
The light diffuses into its component colors when it emerges from the prism at a slightly different angle.
White light is not harmful.
White light is composed of many colors.
Each of the colors has different frequencies and wavelength.
The figure above shows the angle of incidence of the incident beam.
The beam can be seen when it enters the prism and when it leaves.
The minuscule variation in n for light in air will not be taken into account.
Unless you are specifically addressing dispersion, n will be given as a single number, regardless of color.
The beam of light bends away from the normal when it strikes a medium with a lower index of refraction.
When the angle of incidence reaches a critical angle, the angle of refraction becomes 90 degrees, which means the beam is directed along the surface.
The entire beam is reflected back into the original medium if the angle of incidence is greater than th c. The phenomenon is called total internal reflection.
The incidence ray is n 1 or q 1 and means where the source comes from.
The resulting ray should be treated as n 2 or q 2.
If n 1 and n 2 are the same, total internal reflection can't happen.
The largest output of sin th is 1, so the largest input of sin th is 1.
If the angle of incidence is larger than the critical angle, then total internal reflection is a possibility.
When the light source is in the water and the light strikes the boundary of the medium with a lower Refractive index, total internal reflection can occur.
If the light from the water strikes the water/air boundary at an angle of incidence greater than 49deg, total internal reflection will occur.
If the light ray undergoes total internal reflection, you need to check it.
If it undergoes total internal reflection, there will be no rays.
There is no angle of refraction for a situation that undergoes total internal reflection.
The light must be transmitted into the air from the water in order for the fisherman to see it.
The figure shows that the light from the flashlight will come from the water.
The angle of incidence is greater than the critical angle, and the light would be reflected back into the water, rendering it invisible to the fisherman above.
The index for the glass is 1.55.
If th 2 is less than 20deg, total internal reflection will take place.
If th 1 is smaller than 32deg, total internal reflection will occur at the right-hand face of the prism.
A mirror is an optical device that reflects light.
The purpose of this section is to analyze the images that we have looked into a mirror and seen nearby objects.
The simplest type of mirror is a plane mirror.
We will have to use mathematical methods or equations to analyze the patterns of reflection from curved mirrors.
The figure below shows an object in front of a mirror.
Light that's reflected off of an object is reflected back to us.
The direction of the rays reflected off the mirror affects our perception of the image.
When we look at ourselves in a mirror, it seems like our image is behind the mirror, and if we take a step back, our image also takes a step back.
The Law of Reflection can be used to show that the object in front of the mirror is not as far behind the mirror as the image is.
This answers the question.
If light rays focus at the image, it is said to be real.
A screen can show a real image.
Light rays bounce off the front of the mirror, so there is no light behind it.
The images produced by a flat mirror are not real.
This answers the second question.
Flat mirrors produce upright images when we look into them, and question (3) is answered.
The image formed by a flat mirror is not affected by the size of the object.
This answers a question.
A spherical mirror is a mirror with a curved surface that forms part of a sphere.
The mirror's center of curvature is the center of the imaginary sphere, and the mirror's radius is R.
If the mirror had a cross-section, any rays parallel to the axis would be reflected by the mirror through the focal point.
The shapes of a spherical mirror and a parabolic mirror are nearly the same, so they do this for light rays near the axis.