Physics - Chapter 8 - Light & Optics

What are the major differences between lenses and mirrors?

1. Lenses refract light while mirrors reflect light 2. Light is refracted twice when passing through a lens (ie for someone wearing glasses, light travels from an object through the air into the glass lens (1st surface), then it travels through the glass until it reaches the other side where it travels out of the glass and back into the air (2nd surface). This the light is refracted twice as it passes from air to lens and from lens back to air. 3. A lens has 2 focal points (because light can travel from either side of the lens.

What 3 rays do you always draw to determine where an image is for mirrors?

1. Ray Parallel to Axis (green) -> reflects back through focal point 2. Ray through focal point (red) -> reflects back parallel to axis 3. Ray to center of mirror (blue) -> reflects back at same angle relative to normal

What rays are always drawn in a ray diagram?

1. Ray parallel to the axis -> reflects back through focal point (green) 2. Ray through focal point -> reflects back parallel to axis (red) 3. Ray to center of mirror -> reflects back at same angle relative to normal (blue) *Figures on page 277

What is the speed of light in air?

3 x 10^8 m/s

What is the speed of light?

3x10^8 m/s

What wavelengths does the visible light spectrum fall under?

400nm - 700nm **remembering this will save you time on test day!

A red object under blue light will appear __. Why?

A red object under blue light will appear black. Because, a red object in regular white (all colors) light is absorbing every color except red (which it reflects). If you put the red object under blue light, it will continue to absorb the blue light, but it will no longer have red light to reflect and thus will not reflect any light and therefore appears black (which is the absence of light).

What are lenses in contact?

A series of lenses with negligible distances between them

What kind of image does a diverging mirror produce?

A single diverging mirror forms only a virtual, upright, reduced image, regardless of the position of the object

An object that appears yellow is one that absorbs __ and reflects __

A yellow object absorbs all colors of light and reflects yellow

What is total internal reflection?

All reflected light stays within a medium. (c) in our image

An object is placed 6cm in front of a concave mirror that has a 10 cm radius of curvature. Determine the image distance, the magnification, whether the image is real or virtual, and whether it is inverted or upright.

Answers: -Image is +30cm in front of the mirror -Image is real, inverted, enlarged

What is the center of curvature of a spherical mirror?

Assume that the spherical mirrors were cut from a sphere. The point in the center of the sphere that the mirror was cut from is known as the center of curvature and is denoted by the letter C in the diagram.

Where is C for a convex mirror?

C = center of curvature (this is where the center of the sphere would be if the mirror was cut from a sphere) C is behind convex mirrors

Where is C for a concave mirror?

C = center of curvature (this is where the center of the sphere would be if the mirror was cut from a sphere) C is in front for concave mirrors

__ are diverging lenses

Concave

__ are also called converging mirrors. Why?

Concave = Converging because they cause parallel incident light rays (those traveling parallel to the axis the object is sitting on) to converge

How can you find where an image is for a concave lens?

Concave = Diverging Lens Draw the following rays and find a point where any two intersect. This point of intersection parks the tip of the image. 1. Ray 1 is parallel to the optical axis & exits along the line that passes through the focal point on the same side of the lens 2. Ray 2 passes through the center of the lens and is not deviated. 3. Ray 3 approaches along the line that passes through the focal point on the opposite side (if it were to keep going straight), but exits the lens parallel to the axis Good Source: https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses

What image is produced when an object is placed at the focal point of a converging mirror?

Converging mirror = Concave mirror Object at focal point = no image created because the reflected rays are parallel & thus do not intersect (example (b) in graph)

What image is produced when an object is placed between the focal point and a converging mirror?

Converging mirror = Concave mirror Object between focal point & concave mirror = virtual, upright, and magnified (example (c) in graph)

What image is produced when an object is placed beyond the focal point of a converging mirror?

Converging mirror = Concave mirror Object beyond focal point = real, inverted, magnified (example (a) in graph)

__ are converging lenses

Convex

How can you find where an image is for a convex lens?

Convex = Converging Lens Draw the following rays and find a point where any two intersect. This point of intersection parks the tip of the image. 1. Ray 1 enters the lens parallel to the optical axis and passes through the focal point on the opposite side. 2. Ray 2 passes through the center of the lens and is not deviated. 3. Ray 3 passes through the focal point on its way to the lens and exits the lens parallel to the optical axis. Good Source: https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses

__ are also called diverging mirrors Why?

Convex = Diverging because they cause parallel incident light rays (those traveling parallel to the axis the object is sitting on) to diverge

What is the equation for the speed of an electromagnetic wave?

Electromagnetic waves travel at the speed of light so... c = f•λ c - speed of light (3x10^8 m/s) f - frequency of the wave λ - wavelength of the wave

What type of lens is used for people who are farsighted? What is farsightedness called?

Farsighted people = people who can see distance, but need glasses for up-close (reading glasses) Farsightedness = hyperopia These are converging (convex) lens glasses

What is the lensmaker's equation? What is it used for?

For lenses where the thickness cannot be neglected, the focal length is related to the curvature of the lens surface and the index of refraction of the lens by the lensmaker's equation: 1/f = (n-1)([1/r1] - [1/r2]) n - index of refraction of the lens material r1 & r2 - radius of curvature of the first & second lens surfaces, respectively f - focal length

Concave vs Convex and Converging vs Diverging for Lenses vs Mirrors

Mirrors: Concave = Converging Convex = Diverging Lenses: Concave = Diverging Convex = Converging *mirrors and lenses are opposites of each other

What is the order of the electromagnetic spectrum?

Mnemonic: Rotten Men Inevitabily Visit Ugly X Girlfriends ----- (lowest freq) Radio Microwave IR Visible UltraViolet X-Rays Gamma Rays (highest freq)

What type of lens is used for people who are nearsighted? What is nearsightedness called?

Nearsighted people = people who can see up-close, but need glasses for distance (ie you) Nearsightedness = myopia These are diverging (concave) lens glasses

What is the sign convention for a single mirror?

Note: -The focal length of converging mirrors (and converging lenses) is always positive. -The focal length of diverging mirrors (and diverging lenses) is always negative.

One of the distinguishing features of __ images is the ability of the image to be projected onto a screen

One of the distinguishing features of real images is the ability of the image to be projected onto a screen ie a real image can be projected/focused onto the retina (a "screen") Because... Real images are those where light actually converges, whereas virtual images are locations from where light appears to have converged.

Plane mirrors always create __ images. Why?

Plane mirrors always create virtual images. Remember, virtual images are those where light did not actually converge to make the image. ie The image (I) in the diagram is a virtual image because the light rays from the object (O) did not actually converge to make the image. Because plane mirrors cause neither convergence nor divergence of reflected rays - the rays simply just bounce back off of the plane mirror at opposite θ that they hit it with

What is the power of a lens?

Power (P) is measured in diopters P = 1/f P - power (units = diopters) f - focal length (in meters)

__ light is highest frequency, shortest wavelength

Purple **remembering this will save you time on test day!

What is the difference between a real vs. virtual image?

Real images are those where light actually converges, whereas virtual images are locations from where light appears to have converged. One of the distinguishing features of real images is the ability of the image to be projected onto a screen (ie a real image can be projected/focused onto the retina (a "screen"))

__ light is lowest frequency, longest wavelength

Red **remembering this will save you time on test day!

What is the critical angle?

The critical angle (θc) is defined as the angle of incidence (θ1) that provides an angle of refraction (θ2) of 90-degrees. (aka when θ2 = 90˚) At θc, the refracted light ray passes along the interface between the two media.

What is the difference between a real & virtual object in mirrors vs lenses?

The designations of real and virtual are confusing for students because they are on opposite sides for mirrors and lenses. Remember: the real side is where light actually goes after interacting with the lens or mirror. For mirrors, light is reflected and thus stays in front of the mirror. So, the real side is in front of the mirror & virtual is behind the mirror. For lenses, light is refracted and thus travels through the lens. So, the real side is on the side opposite to the original light source & the virtual side is on the same side as the original light source (ie if the object is behind the lens and the image ends up in front of the lens, then the image is real). Lenses shown in image diagram.

Describe the refractive surfaces in the eye.

The eye is a complex refractive instrument that uses real lenses. The cornea acts as the primary source of refractive power because the change in refractive index from air is so significant. Then, light is passed through an adaptive lens that can change its focal length before reaching the vitreous humor. it is further diffused through layers of retinal tissue to reach the rods and cones. At this point, the image has been focused and minimized significantly, but is still relatively blurry. Our nervous system processes the remaining errors to provide a crisp view of the world.

What is the focal point of a mirror?

The focal point of a lens or mirror is the point in space where parallel light rays meet after passing through the lens or bouncing off the mirror. A "perfect" lens or mirror would send all light rays through one focal point, which would result in the clearest image.

What equations can you use for finding image distance and magnification for lenses?

The same basic formulas for finding image distance and magnification for spherical mirrors also apply to lenses. So, 1/f = 1/o + 1/i = 2/r and m = -i/o f - focal length o - object distance i - image distance r - radius of curvature

For __ lenses, the focal lengths are equal.

Thin Spherical Lenses (ie converging & diverging lenses)

What type of waves are electromagnetic waves? Why?

Transverse Waves because the electric field wave and the magnetic field wave are perpendicular to the direction the wave is propagating

What is the equation for the index of refraction of a material?

When light is in any medium besides a vacuum, its speed is less than c (3x10^8 m/s, which is speed of light in vacuum). Equation for Index of Refraction: n = c/v n - index of refraction c - speed of light in vacuum (3x10^8) v - speed of light in the given medium ie the Index of refraction for water is n = 1.33

When light enters a medium with a lower index of refraction, it bends __ relative to the normal

away from the normal (ie when light goes from water (n = 1.33) to air (n = 1.0))

What is black?

black is the absence of all light (since white light is all the lights together, black is the absence of all light)

Where is θ1 and θ2 in a snell's law diagram?

both angles are taken between the ray and the normal

What does a concave mirror look like?

concave caves in

What is a diverging lens?

concave lens

What is a convex lens?

converging lens

What is a converging lens?

convex lens

What is a concave lens?

diverging lens

What is the equation used to calculate image distance?

f - focal length o - distance between object & mirror i - distance between image & mirror r - radius of curvature *this equation can be used for all types of lenses and mirrors!

The focal length of diverging mirrors (and diverging lenses) will always be negative/positive

f = always negative for diverging (convex) mirrors & lenses

The focal length of converging mirrors (and converging lenses) will always be negative/positive

f = always positive for converging (concave) mirrors & lenses

What is the equation for focal length for spherical mirrors?

f = r/2 f - focal length r - radius of curvature

What is hyperopia?

farsightedness (you are able to see distance, but not up-close)

What type of lens is used to correct farsightedness?

farsightedness = hyperopia converging lens

What is focal length?

focal length = f the distance between the focal point (F) and the mirror

What does an electromagnetic wave look like?

has an electric field wave (E) and has a magnetic field wave (B)

When you have hyperopia, where does light focus in respect to the retina?

hyperopia = farsightedness (you are able to see distance, but not up-close) light focuses behind the retina

What is the equation for image location of a plane mirror?

i = -o So, the virtual image is at a distance behind the mirror equal to the distance the object is in front of the mirror (ie if the object is 5m in front of the plane mirror, then the virtual image is 5m behind the plane mirror)

If magnification is (-), then the image is __

inverted (upside down)

If |m| > 1, then the image is __

larger than the object *|m| is absolute value of m, magnification

What is the focal length for lenses in contact? Power?

lenses in contact = a series of lenses with negligible distances between them

__ refract light while __ reflect light

lenses refract light mirrors reflect light

If the angle of incidence is less than the critical angle __

light bends away from the normal (a) in diagram

If the angle of incidence is equal to the critical angle __

light refracts at 90˚ to the normal (b) in diagram

What is the equation for magnification?

m = -i/o m - magnification (unitless) i - distance between image & mirror/lens o - distance between object & mirror/lens *used with mirrors & lenses!

What is myopia?

myopia = nearsightedness (you are able to see up-close, but not distance ... aka your vision)

When you have myopia, where does light focus in respect to the retina?

myopia = nearsightedness (you are able to see up-close, but not distance ... aka your vision) light focuses in front of the retina

What is Snell's Law?

n1sinθ1 = n2sinθ2 Refracted rays obey this law. n1 & θ1 - medium from which the light is coming in (ie air in our image) n2 & θ2 - medium into which the light is entering (ie water in our image)

What type of lens is used to correct nearsightedness?

nearsightedness = myopia diverging lens

__ cause neither convergence nor divergence of reflected light rays

plane mirrors (so light that hits a plane mirror will be reflected back at the same angle it hit the plane mirror with and thus if two light beams are emitted from one object at different angles, they will hit and reflect from the plane mirror at those angles and will not converge)

If an image has a positive distance (i > 0), it is a __ image and the image is __ (location)

real in front of mirror

For a single lens or mirror, inverted images are always __

real think: inverted, real-> IR

__ is the bending of light as it passes from one medium to another and changes speed

refraction

If |m| < 1, then the image is __

smaller than the object *|m| is absolute value of m, magnification

What speed do electromagnetic waves travel at?

speed of light! (3x10^8 m/s)

What is the radius of curvature?

the distance between C (center of curvature) and the mirror

For a thin lens, the sign of the focal length and radius of curvature are given based on __

the first surface the light passes through

In a vacuum, all electromagnetic waves travel at __

the same speed - the speed of light!

What does a converging lens look like?

thicker at the center (think about how the edges look like a 'C')

What does a diverging lens look like?

thinner at the center (think about how the edge look slike the front of a D)

If the angle of incidence is greater than the critical angle __

total internal reflection occurs (c) in diagram

When light enters a medium with a higher index of refraction, it bends __ relative to the normal

towards the normal (ie when light goes from air (n = 1.0) to water (n = 1.33))

If magnification is (+), then the image is __

upright (same direction as object)

__ has the lowest index of refraction

vacuum (n = 1.0) and then air (n = 1.0003), which is considered vacuum in our problems to simplify things

If an image has a negative distance (i < 0), it is a __ image and the image is __ (location)

virtual behind the mirror

For a single lens or mirror, upright images are always __

virtual think: upright, virtual -> UV

What has a higher index of refraction: air or water?

water has a higher index of refraction (n = 1.33) air is essentially the same as a vacuum in terms of light-related things and any medium besides a vacuum/air will have a higher index of refraction

What is rectilinear propagation?

when light travels through a homogeneous medium, it travels in a straight line

Light that contains all the colors in equal intensity is perceived as

white

What is the equation for angle of light reflection?

θ1 = θ2 both θs are measured from the normal (the line drawn perpendicular to the boundary of the reflective medium)

What is the equation for the critical angle?

θc - critical angle n1 & n2 - index of refraction of the media the light is initially in and ends up in (respectively)