Chapter 8: Optics Flashcards
What is the electromagnetic spectrum? What is the wavelength of visible light?
The electromagnetic spectrum includes the full range of frequencies and wavelengths of electromagnetic waves including radio, micro, IR, visible, UV, X, gamma in order of lowest frequency (longest wavelength, lowest energy) to highest frequency (shortest wavelength, highest energy).
Visible light is from 750 to 380 nm (7.5-3.8x10^-7m)
What are the colors of the visible spectrum? What are their wavelengths?
Red: 750-620 nm
Orange: 620-590 nm
Yellow: 590-560 nm
Green: 570-500 nm
Blue: 495-450 nm
Violet: 450-380 nm
Are electromagnetic waves transverse or longitudinal waves?
Electromagnetic waves are transverse waves because the oscillating electric and magnetic field vectors are perpendicular to the direction of propagation. The electric field and magnetic field are also perpendicular to each other.
What is the speed of light? What is the equation for speed of light in a vacuum?
This is the speed of light in the vacuum, but for the purpose of MCAT related questions is also a good approximation for the speed of light in air.
What is white light? What makes us perceive something as red (or having a color)?
Light that contains all the colors and equal intensity as perceived as white.
The color of an object that does not admit its own light is dependent on the color of light that it reflects. Thus, an object that appears red is one that absorbs all colors of light except red. This implies that a red object under green illumination will appear black because it absorbs the green light and has no light to reflect.
What is a blackbody?
The term blackbody refers to an ideal absorber of all wave lengths of light, which would appear completely black if it were at a lower temperature than its surroundings.
MCAT concept check electromagnetic spectrum 8.1 page 288
Order the types of electromagnetic radiation from highest energy to lowest energy. What other property of light follows the same trend?
Gamma, x, ultraviolet, visible, infrared, micro, radio.
The higher the frequency, the more energy, conversely, the longer the wavelength, the lower the energy.
MCAT concept check electromagnetic spectrum 8.1 page 288
True or false. Light waves are longitudinal because the direction of propagation is perpendicular to the direction of oscillation.
False. Light waves are transverse because the direction of propagation is perpendicular to the direction of oscillation.
MCAT concept check electromagnetic spectrum 8.1 page 288
What are the boundaries of the visible spectrum? How does the range of the visible spectrum compared to the range of the full electromagnetic spectrum?
The full electromagnetic spectrum ranges from wavelengths of nearly 0 to 10^9 meters.
What is rectilinear propagation? What is geometric optics?
Rectilinear propagation is the tendency of light to travel in a straight line.
When light travels through a homogenous medium, it travels in a straight line. This is known as rectilinear propagation. The behavior of light at the boundary of a medium or interface between two media is described by the theory of geometrical optics. Geometrical optics explains reflection and refraction, as well as the applications of mirrors and lenses.
What is reflection? What is the law of reflection? What is the normal line?
Reflection is the rebounding of incident light waves at the boundary of a medium. Light waves that are reflected are not absorbed into the second medium rather they bounce off of the boundary and travel back through the first medium.
What is the real image? What is a virtual image?
What is the distinguishing feature of real images?
An image is said to be real if the light actually converges at the position of the image.
An image is virtual if the light only appears to be coming from the position of the image, but does not actually converge there.
One of the distinguishing features of real images is the ability of the image to be projected onto a screen.
Do plane mirrors create virtual images?
Parallel incident light rays remain parallel after reflection from a plane mirror; that is plane mirrors being flat reflective surfaces, cause neither convergence nor divergence of reflected light rays.
Because the light does not converge at all, plain mirrors always create virtual images.
Why do plane mirrors only create virtual images?
In a plane mirror, the image appears to be the same distance behind the mirror as the object is in front of it. In other words, plane mirrors create the appearance of light rays originating behind the mirrored surface. Because the reflected light remains in front of the mirror, but the image appears behind the mirror, the image is virtual.
Can plane mirrors be conceptualized as spherical mirrors with an infinite radius of curvature?
Plane mirrors can be conceptualized as spherical mirrors with an infinite radius of curvature. Silly card.
Give an example of a convex mirror and a concave mirror.
A convex mirror example would be a passenger side mirror in a car (objects in mirror are closer than they appear). Everything appears smaller and farther away in a convex mirror.
Concave mirror example would be small circular mirror is used for applying make up. Everything appears bigger and closer in a concave mirror.
What are two types of spherical mirrors? Why are they called spherical mirrors?
The two variety of spherical mirrors are concave and convex.
The word spherical implies that the mirror can be considered a spherical cap or taking from a much larger spherically shaped mirror.
If we were to look from the inside of the sphere to its surface, we would see a concave surface. On the other hand, if we were to look from outside this sphere, we would see a convex surface.
How are spherical mirrors described (C and r)?
Spherical mirrors have an associated center of curvature (C), and a radius of curvature (r).
The center of curvature is a point on the optical axis located at a distance equal to the radius of curvature from the vertex of the mirror.
THE CENTER OF CURVATURE WOULD BE THE CENTER OF THE SPHERICALLY SHAPED MIRROR IF IT WERE A COMPLETE SPHERE.
What is a converging mirror, what is a diverging mirror?
Concave mirrors are called converging mirrors, convex mirrors are called diverging mirrors.
They are called this because they cause parallel incident light rays to converge and diverge after they reflect, respectively.
What is the focal length (f)?
The focal length (f) is the distance between the focal point (F) and the mirror.
What is the focal length for all spherical mirrors?
For all spherical mirrors, the focal length is half of the radius, where the radius of curvature (r) is the distance between center of curvature (C) and the mirror.
What are the important lengths associated with mirrors? Draw the key variables in geometric optics (without light rays).
C: center of curvature
r: radius of curvature (distance from C to mirror)
F: focal point
f: distance between focal point and mirror (f=r/2 for vehicle mirrors)
O: object
o: distance between O and mirror
I: image
i: distance between I and mirror
What is the relationship between the four distances for geometrical optics?
What image image distance (i)? What does it mean when i is greater than zero? What does it mean when i is less than zero?
i is the image distance, the distance between the image and the mirror.
If i>0 it is a real image, implying that the image in front of the mirror.
If i<0 it is a virtual image and thus located behind the mirror.
Plane mirrors can be thought of as spherical mirrors with infinitely large focal distances what does this mean for the nature of the image and the distance from o to i?
As such, for a plane mirror, r=f=infinity and the equation becomes 1/o+1/i=0, or o=-i.
This can be interpreted as saying the virtual image is a distance behind the mirror equal to the distance the object is in front of the mirror.
What is magnification?
This card is incorrect. Fix it.
Magnification is the ratio of the image distance to the object distance (and is therefor dimensionless).
Magnification also gives us the ratio of the size of the image to the size of the object.
m=-i/o
Draw the image formation by a plane mirror.
Draw perpendicular ray and ray to normal.
When drawing a ray diagram, there are three important rays to draw. What are they?
For a concave mirror, a ray that strikes the mirror parallel to the axis is reflected back through the focal point (GREEN LINES).
A ray that passes through the focal point before reaching the mirror is reflected back parallel to the axis (RED LINES).
A ray that strikes the mirror at the point of intersection with the axis is reflected back with the same angle measured from the normal (BLUE LINES).
For a convex mirror, what can be said about the image if:
The object placed beyond F (o greater than f)
The object is placed at F
The object is placed between F and the mirror (o is less than r)
If the object is placed beyond F, the image will be real, inverted, and magnified.
If the object is placed at F , no image is formed because the reflected light rays are parallel to each other.
If the object is placed between F and the mirror, the image produced is virtual, upright, and magnified.
Draw ray diagrams for a concave mirror and describe the three circumstances and outcomes of the image.
What are the three possible outcomes for an object placed in front of a concave mirror?
If the object is placed beyond the focal point, the image will be real, inverted, and magnified.
If the object is placed on the focal point, the image will be at infinity.
If the object is placed between the focal point and the mirror, the image will be virtual upright and magnified.
What is the only image outcome for a single diverging mirror?
What happens to the image the farther away the object is from the mirror?
A single diverging mirror forms only a virtual, upright, and reduced image, regardless of the position of the object.
The farther away the object, the smaller the image will be.
Describe a mirror seen in a convenience store (security mirror).
A security mirror is a convex, diverging optical system. Parallel light ray that hit the mirror or reflected in multiple directions, which allows the observer to see a large field vision, even if the image is somewhat distorted, and the objects in the image are closer than they appear. A passenger side mirror of a car is also a convex mirror, allowing the driver to see a wider view of the other vehicles behind the car (images looking closer than they appear).
Draw a ray diagram for a convex (diverging) mirror. How many different diagrams do we need to draw to demonstrate the circumstances of image and object of a convex mirror?
We really only need to draw one way a diagram for convex (diverging) mirrors as the image will always be the virtual, upright, and reduced regardless of the position of the object.
When drawing a ray diagram, what are the three important rays to draw?
A ray that strikes the mirror parallel to the axis, a ray that passes through the focal point before reaching the mirror, a ray that strikes the mirror at the point of intersection with the axis.
Again. What are the three major rays to draw when drawing a ray diagram? Draw ray diagram for a concave (converging) mirror. Describe the images produced.
Draw a diagram for a convex (diverging) mirror.
Book concept to find where the image is for a mirror.
What is the sign for the focal length for converging (concave)mirrors and converging lenses? What is the sign for the focal length for diverging (convex) mirrors and diverging lenses?
The focal length of converging mirrors and converging lenses will always be positive.
The focal length of diverging mirrors and diverging lenses will always be negative.
Is a convex mirror converging or diverging? Why?
Is a concave mirror converging or diverging? Why?
Do convex mirrors make real or virtual images?
A convex mirror is diverging because when light rays hit its curved surface, they spread out or diverge away from each other.
A concave mirror is converging because when light rays hit its curve surface, they converge the light rays toward a focal point.
Convex mirrors always produce virtual images, meaning the image appears to be behind the mirror and cannot be projected onto a screen.
What is the sign convention for a single mirror for symbols o, i, r, f, and m? Which symbol is almost always positive?
For clarification:
i is positive for real images (in front of mirror) and negative (behind mirror) for virtual images.
r is positive for concave (in front of mirror) and negative for convex (behind mirror). (r is related to the focal point, f=r/2)
f is positive for concave/converging mirror (in front of mirror) and negative for convex/diverging mirror (behind mirror) f=r/2
Positive m: upright; negative m: inverted
The object distance o is almost always positive (which means that the object is placed in front of the mirror)
Example of geometrical optics page 293
For a single mirror or lens with o>0, a real image will always be inverted. We we needed to extrapolate this based on our knowledge of concave mirrors.
We needed to use the optics equation and recognize the variables given to solve for i (image distance).
Mnemonic in the book for image types with single lens or mirror: UV NO IR
Upright images are always Virtual
NO images formed when the object is a focal length away.
Inverted images are always Real
What does (-)m mean? (+)m? Absolute value of m being greater than 1? Less than one?
Inverted
Upright
Larger
Smaller
What is refraction? Does the speed of light change in a medium?
Refraction is the bending of light as it passes from one medium to another and changes speed.
The speed of light through any medium is always less than its speed through a vacuum, but in air is really really really close to 3×10^8 m/s.
What is the equation for speed of light in a medium besides a vacuum? What is the index of refraction? What is the index of refraction of a vacuum?
The index of refraction is a dimensionless quality that describes the ratio between the speed of light in a vacuum, and the speed of light in a medium.
The index of refraction of a vacuum, by definition, is one. For all other materials, the index of refraction will be greater than one.
What is Snell’s law? What is the equation for Snell’s law?
Refracted rays of Lido base no laws they passed from one medium to another.
What happens when light enters a medium with a higher index of refraction? What happens when light enters a medium with a lower index of refraction?
When light enters a medium with higher index of refraction, it bends toward the normal.
When light enters a medium with lower index of refraction, it bends away from the normal.
Using the equation for Snell’s law, show which way light bends given different indices of refraction.
Think of a straw in a glass of water. How can this help us remember which way light will bend when entering a medium with a higher index of refraction.
Index of refraction problem, page 296
The mathematics on this equation or way outside of the scope of the MCAT. This question is provided mainly as an opportunity to see the application of Snells law.
What is total internal reflection? When does total internal reflection occur?
When light travels from a medium with a higher index of refraction (such as water) to a medium with a lower index of refraction (such as air), the refracted angle is larger than the incident angle. That is, the refracted light ray bends away from the normal. As the incident angle is increased, the refracted angle also increases, and eventually, a special incident angle called the critical angle is reached for which the reflected angle equals 90°. At the critical angle, the refracted light ray passes along the interface between the two media.
What do the ray diagrams for single lenses look like (convex converging and concave diverging)?
What is the difference between lenses and mirrors?
Aside from the fact that lenses transmit light while mirrors reflect it, there are two surfaces that affect the light path with lenses. The light is reflected twice as it passes from air to lens and from lens back to air.
Are reading glasses diverging or converging lenses?
This is sort of a trick question.
Farsighted means nearby objects are blurry. Reading glasses are needed by people who are “farsighted” and are converging lenses.
Nearsighted means far away objects are blurry. Standard glasses are needed by people who are “nearsighted” and are diverging lenses.
How many focal points does a lens have?
Because light can travel from either side of lens, lens has two focal points, with one on each side. The focal lengths can be measured in either direction from the center. For thin spherical lenses, the focal links are equal, so we speak of just one focal length for the lens as a whole.
Draw the ray diagrams for single lenses. How many of them are there? What is similar between all of them?
Similarity is that the distance between the focal point and mirror, f, are all equal.
Draw a ray diagram for a concave mirror where the object is placed beyond the focal point.
Draw a ray diagram for a concave mirror where the object is on the focal point.
Draw a ray diagram for a concave mirror where the object is placed in front of the focal point (between F and mirror)
Draw a ray diagram for a concave mirror.
What is near sightedness? How do we solve nearsightedness with a lens?
Nearsightedness is when the converging lens of your eye focuses images in front of your retina. If you place a diverging lens in front of your eye, which moves the rays apart and refocuses the image on your retina.
What is farsightedness? How do we solve farsightedness with a lens?
What is farsighted? What is nearsighted?
Farsighted means near objects are blurry. Need converging lens in front of eye. Lens of eye converges rays behind the retina.
Nearsighted means far objects are blurry. Need diverging lens in front of eye. Lens of eye converges rays in front of retina.
Describe converging and diverging lenses in terms of thickness at the center of the lens.
Converging lenses are thicker in the center, diverging lenses are thinner in the center.
What is the equation that relates object distance (o), image distance (i), focal length (f) and magnification for lenses?
Draw a ray diagram for a converging lens with o>f.
What are the signs for i, r, f, and m?
Draw ray diagram for converging lens with o<f.
What are the signs for all the relative symbols for this diagram? (i, o, r, f, m)
Draw a ray diagram for a concave (diverging) lens with r>f.
Signs for the symbols.
The image will always be virtual and upright.
What is the sign convention for lenses (positive and negative negative i, o, r, f, m)?
What side is the Real side for a mirror? What side is the Real side for a lens?
The Real side of a mirror is in front of the mirror.
The Real side for a lens is the other side of the lens from the light source.
How do we find where an image is for a lens using a ray diagram?
For rays where thickness cannot be neglected, we use the lens makers equation. What is are?
This equation demonstrates how to calculate f for a lens where thickness cannot be ignored (a real lens). It depends on the index of refraction for the lens, and the difference of the inverse of radius of curvature of first and second lens.
Optometrists describe lenses in terms of power. What is the equation for power of focal length?
What is a multiple lens system? Give an example of a multiple lens system. How do multiple lens systems behave? What is the equation for f and P of a multiple lens system?
For lenses not in contact, the image of one lens becomes the object of another lens. The image from the last lens is considered the image of the system. Microscopes and telescopes do this. How do we calculate the magnification of such a system?
Example for diverging lens page 302
What is spherical aberration?
Spherical mirrors and lenses are imperfect and subject to specific types of errors or aberrations.
Spherical aberration is a blurring of the periphery of an image as a result of inadequate reflection of parallel beams at the edge of a mirror or inadequate refraction of parallel beams at the edge of a lens.
What is dispersion?
Dispersion is where various wavelengths of light separate from each other, like light through a prism.
The index of refraction of a medium affects the wavelength of light passing through the medium because the index of refraction is related or the speed of the wave by n=c/v. It also implies that the index of refraction itself actually varies with the wavelength.
When white light passes through a prism, what happens to the light? Is there a pattern to this? Why?
When light passes through a prism, IT REFRACTS, and the light disperses into various wavelengths and therefor colors.
Violet light has the smallest wavelength and therefor experiences the greatest amount of refraction among the colors of the visible spectrum.
Red light has the longest wavelength and therefor experiences the least amount of refraction among the colors of the visible spectrum.
Because of this, the pattern that emerges is the red comes out on top and violet emerges on the bottom.
When light enters a medium, with a different index of refraction, the wavelength changes. Does this mean that the frequency of light also change?
As light enters a medium with a different index of refraction, the wavelength changes but the frequency of the light does not.
What is chromatic aberration?
Chromatic aberration is a dispersive effect within a spherical lens.
MCAT concept check geometrical optics 8.2 page 305 question 1
MCAT concept check geometrical optics 8.2 page 305 question 2
True or false. Incident angle is always measured with respect to the normal.
True. In optics, incident angles are always measured relative and to the normal.
MCAT concept check geometrical optics 8.2 page 305 question 3
Light will bend toward normal when going from a medium with low n to a medium with high n.
Light will bend away from normal when going from a medium with high n to a medium of low n.
MCAT concept check geometrical optics 8.2 page 305 question 4
Define dispersion. Define aberration.
Dispersion is the separation of light by wavelength when passing through a medium. Dispersion is the tendency for different wavelengths of light to experience different degrees of refraction in a medium, leading to separation of light into the visible spectrum (a rainbow).
Aberration is a blurring of an image due to imperfections in a lens. Aberration (spherical or chromatic) is the alteration or distortion of an image as a result of an imperfection in the optical system.
MCAT concept check geometrical optics 8.2 page 305 question 5
What are the two mathematical relationships between image distance and object distance?
What is the marching band analogy for reflection of light?
A handy way to determine which way light will refract is to imagine a marching band entering a plot of sand. The line of musicians nearer to the plot of sand will slow down first, the line of musicians will reach the sand later. Look it up if you need an example.
What is light diffraction?
Light diffraction refers to the spreading out of light as it passes through a narrow opening or around an obstacle.
Think “diff” is diffuse
What is single slot diffraction?
What is a slit lens system? What is the equation for a slit lens system?
What is the equation for the location of the dark fringes (minima) in a slit lens system?
Find and draw a better representation of this phenomena.
What do we call dark fringes in a slit lens system or multiple slit system? Bright fringes?
Dark fringes are minima and bright fringes are called maxima.
If n is a dark fringe (minima) in a slit lens system, what would a bright fringe (maxima) be?
n+0.5 as bright fringes (maxima) are halfway between dark fringes (minima)
Double slit example page 309
Need to recognize that we aren’t given the hypotenuse. We can make an assumption that the distance between the screen and the slits is approximately equal to the hypotenuse, and can substitute sintheta=tantheta.
Recognize that when calculating deltan, the 1/2 cancels.
Is math from there.
What is a diffraction gratings?
Diffraction gratings consist of multiple slits arranged in patterns. They create colorful patterns similar to a prism as the different wavelengths interfere in characteristic patterns. Thin films cause interference patterns because light waves reflecting off the external surface interfere with light waves reflecting off the internal surface of the film.
MCAT concept check 8.3 diffraction page 311 question 1
How does the defraction pattern for a single slit differ from a slit with a thin lens?
Diffraction through a single slit does not create characteristic fringes when projected on a screen, although the light does spread out. When a lens is introduced into the system, the additional refraction of light causes constructive destructive interference, creating fringes.
MCAT concept check 8.3 diffraction page 311 question 2
What wave phenomenon do defraction fringes result from?
Fringes result from constructive and destructive interference between light rays.
How does double slit diffraction and interference differ from single slit diffraction?
The image formed during double slit diffraction contains fringes because light rays constructively and destructively interfere. A single slit forms an image of a wide band of light, spread out from its original beam.
MCAT concept check 8.3 diffraction page 311 question 4
True or false. Maxima in defraction patterns are always equidistant between two minima.
True. Maxima and minimum alternate in a diffraction pattern. A maximum is equidistant between two minima, and a minimum is equidistant between two maxima.
MCAT concept check 8.4 polarization page 313 question 1
Contrast plain polarized and circularly polarized light.
Plane polarized light contains light waves with parallel electric field vectors. Circularly polarized light selects for a given amplitude and has a continuously rotating electric field direction.
MCAT concept check 8.4 polarization page 313 question 2
How does the application of a polarized filter impact the wavelength of light passing through the filter?
Plain polarization has no effect on the wavelength (or frequency or speed) of light. Polarization does affect the amount of light passing through medium and light intensity.
MCAT mastery Optics page 282 question 1
MCAT mastery Optics page 282 question 2
MCAT mastery Optics page 282 question 3
Two ways to do this problem.
Draw a ray diagram. If done properly, you will get a real inverted magnified image. Drill and kill this until you know this.
Use sign convention. If the object is at the center of curvature, its distance is 2f. Plug into the optics equation. i ends up positive, and therefor real.
FOR SINGLE MIRRORS OR LENSES, ALL REAL IMAGES ARE INVERTED. (We can also solve for m and end up with a negative number)
MCAT mastery Optics page 282 question 4
This is a plug and play question. Knowing the equation for double slit, we solve for wavelength.
We got stuck in algebra land there and needed to refer to the answer sheet. Get used to this variety of algebra.
MCAT mastery Optics page 282 question 5
We solved this problem analytically.
First off. We know that the frequency of light doesn’t change when going from one medium to another, this eliminates C and D.
Secondly, we know that as light moves from a lower index of refraction to a higher index index of fraction (n increases), the angle of fraction will be smaller than the incident angle (closer to the normal) so sayeth Snells law.
What is sin and cos for 0, 30, 45, 60, and 90°?
MCAT mastery Optics page 282 question 6
Light will not pass through the third polarizer (D).
Plain polarized light is light in which the electric fields of all the waves are oriented in the same direction. Light passing through the first two polarizers will only contain rays with their electric field vectors in the same direction. When it reaches the third polarizer, however, the light will not be able to pass through because all the light rays will be oriented in the direction dictated by the first and second polarizers.
MCAT mastery Optics page 282 question 7
MCAT mastery Optics page 283 question 8
Pay attention to the sign convention here. If f>o, then 1/f - 1/o is negative because a larger denominator means a smaller number and therefore i is negative given 1/f = 1/o + 1/i ……. 1/i = 1/f - 1/o. Negative i means virtual, and virtual images are upright.
MCAT mastery Optics page 283 question 9
What is the equation for the critical angle regarding total internal reflection?
MCAT mastery Optics page 283 question 10
When light passes through a narrow opening, the light wave spread out. As the slit narrows, the light wave spread out even more.
MCAT mastery Optics page 283 question 11
MCAT mastery Optics page 283 question 12
What is sin and cos of 0, 30, 45, 60, and 90°?
MCAT mastery Optics page 283 question 13
MCAT mastery Optics page 283 question 14
Draw diagram. The angle given is respect to the normal you know that the incident angle must be 60°. You know that the reflected beam will have an angle of 60° relative to the normal (law of reflection). We then know the reflected beam will make an angle of 30° with the plain of the glass. If the reflected and refracted beams are perpendicular to each other, the reflected beam will make a 60° angle with the plain of the glass. We can solve for the reflected angle: 30°. Plug and play.
MCAT mastery Optics page 283 question 15
Relevant equations and relationships for chapter 8 optics
