Physics II - Geometric Optics & Reflection

How you find the image on a ray diagram for a convex mirror?

1) Draw a ray parallel to the axis -> reflects back through the focal point 2) Draw a ray through the focal point -> reflects back parallel to axis 3) Draw a ray to the center of the mirror -> reflects back on itself

How you find the image on a ray diagram for a concave lens?

1) Draw a ray parallel to the axis -> refracts and bends away from the focal point 2) Draw a ray through/towards the focal point opposite of the object -> refracts parallel to the axis 3) Draw a ray to the center of the lens -> continues straight through with no refraction Virtual image is created as the viewer perceives the divergence of rays behind the lens coming from a certain point (converging point)

How you find the image on a ray diagram for a convex lens?

1) Draw a ray parallel to the axis -> refracts through a focal point of the front face of the lens 2) Draw a ray through/towards the focal point before reaching the lens-> refracts parallel to the axis 3) Draw a ray to the center of the lens -> continues straight through with no refraction

What are the three different types of bending that can occur when light passes between mediums?

1) Refraction Away or towards the normal 2) Critical Angle Light bends so it is perpendicular to the interface between the mediums 3) Total Internal reflection Light is unable to exit a medium and is instead reflected off of it as though the interface was a mirror.

What is the relationship between the lengths distances described in the ray diagram?

1/f = 1/0 + 1/i = 2/f This equation is often used to find the image distance. If i > 0 = Real image If i < 0 = Virtual image

How many surfaces affect the pathway of light in lenses?

2. Light coming into a lens (e.g. glasses) must first pass from the air into the lens, through the glass, and then from the lens into the air again.

When light travels through a homogeneous medium, it travels in a straight line known as: A) Rectilinear propagation B) Reflection C) Medium D) Normal

A. Rectilinear propagation Reflection is the rebounding of light not absorbed at the boundary of a medium. A medium is the substance that light travels through (e.g. air, water) The normal is a line drawn perpendicular to the boundary of the medium

Light starting in a pool of water with and index of refraction (n = 2) passes through the water and into air. What direction does the light bend as it enters the air?

As the light passes from the water to the air, it bends away from the normal. This is because N2 < N1. This makes sense given Snell's Law. Since N2 is lower, than N1 - given that sin(theta1) can't change - the inverse relationship between N2 and Sin(theta2) dictates that the sin must become greater to accommodate a lower N2.

What happens to the image of an object reflected by a concave mirror when the object is placed: Beyond C? On C? Between C and F? On F? Between F and the mirror?

Beyond C: The image is smaller than the object and inverted. On C: The image is mirrored at the same point as C. Between C and F: The image is larger than the object and inverted. On F: There is no image as the light rays reflect off in parallel directions. This means that the reflected light does not converge. And convergence does not occur at some point behind the mirror to create a virtual image. Between F and the mirror: There is no real image as the reflected light rays spread apart. This spread means that light rays do not converge, but instead diverge from a point behind the mirror (from the viewer's perspective) creating a virtual image.

You are told that a mirror has both it's radius and center of curvature located behind the mirror. What mirror best fits this description. A) Spherical B) Concave C) Convex D) Plane

C. Convex Spherical mirror is a term that includes both convex and concave mirrors

True or False: Because spherical lenses come from conical sections, they are considered perfect lenses.

False. All lenses are subject and prone to errors due to imperfections, known as aberrations. Spherical aberrations are what cause a blurry periphery of an image due to inadequate reflection or refraction. Chromatic aberrations can also happen when white light splits when looking through a lens forming an unnatural colorful halo around an object.

True or False: Refraction is the bending of light in a medium.

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

True or False: Myopia is corrected with converging lenses.

False. Myopia (Nearsightedness) is corrected with diverging lenses. Hyperopia (farsightedness is corrected with converging lenses

How do you quickly determine if the image is virtual or real for a mirror or a lens?

For both mirrors and lens a real image is an image formed at the point where the light light actually converges; these images theoretically could be displayed on a screen. Mirrors: Real images are those that are reflected back on the same side as the object. Virtual images are those that are behind the mirror. Lenses: Real images are those that appear on the opposite side of the lens with the original light source. Virtual images images appear on the same side as the the original light source.

How are lenses described by optometrists?

In terms of Power. It is expressed as: P = 1/f P = Power (Diopters) f = Focal length (meters) (Note: power and focal length share the same sign)

How do multiple lenses in contact behave?

Lenses in contact can be treated as single lenses with their focal length adding up, and their power adding up respectively. An example of lenses in contact are corrective contact lenses.

How do multiple lenses not in contact behave?

Lenses that are not in contact create images that become objects for the next lens, with the last image created being the image of the system. Magnification is the only part that can be calculated. It is expressed as: M = M1 * M2 * M3

What is magnification and how is it calculated? What happens to an image if |m| <>= 1, or if m is <> 0?

Magnification is the ratio of the image distance to the object distance. If |m| > 1 = image is larger than object If |m| < 1 = image is smaller than object If |m| = 1 = image is same size as the object If m > 0 = Image is upright If m < 0 = Image is inverted

What type of mirror exclusively creates virtual images and why?

Plane mirrors create virtual images because they have parallel incident light rays reflecting off of the mirrors remain parallel and niether converge or diverge

What are all the key variables of a ray diagram when observed from a concave parabolic mirror?

Principle axis = Intersection through the middle of the mirror, through C, F, and P P = Pole -> Center of the parabolic mirror C = Center of Curvature F = Focal point = where reflected light from incident rays parallel to the principle axis converge f = r/2 = Focal length = distance between F and P r = 2f = distance between C and P I = Image = point where light converges i = Image distance = distance between I and mirror O = Object = where the object being reflected is o = Object distance = Distance between O and mirror

Concave Mirror

QUESTION

What is the difference between a real image and a virtual image?

Real images are created when light converges at the position of the image. Virtual images are created when light appears to be coming from a position of the image, but light does not actually converge there.

What is Snell's Law

Refers to the principle that as light passes from one medium to the next, it will bend towards or away from the normal depending on the difference in the two medium's index of refraction. It is expressed as: n1 * sin(theta1) = n2 * sin(theta2) When N2 > N1 -> Light bends towards the normal When N2 < N1 -> Light bends away from the normal

What similar signs conventions are shared between single mirrors and lenses?

Single mirrors and lenses both: Have positive r and f if the light is converging; negative if diverging Have upright magnification if positive; inverted if negative

When lens thickness is not negligible, how do you find the focal length?

The Lensmaker's Equation n = Index of refraction r1,2 = radius of curvature for lens surfaces 1 and 2

What is the law of reflection?

The law of reflection states that the incident angle (theta1) = the reflection angle (theta2)

What is the index of refraction?

The speed of light through any medium is less than inside of a vacuum. For any given medium the index of refraction represents the ratio of the speed of light in a vacuum to the speed of light in that medium. Since the speed of light in a vacuum is constant, increases in the speed of light in a medium result in a smaller index; lower speeds result in a larger index. It can be calculated by: n = c/v

How many focal points and focal lengths do converging and diverging lenses have?

They both have two focal points, that are equal in length stretching from each side of the lens to the center of the lens itself. Finding image distance, magnification, object distance, etc uses the same formulas as mirrors: 1/f = 1/0 + 1/i m = -i/o This assumes that the lens length is negligible.

How does total internal reflection occur?

Total angle reflection is a result of the light from a medium with a high index of refraction trying to pass into a medium with a lower index. Due to the relationship of terms in Snell's Law, as the incident angle increases, so does the refracted angle. Once the refracted angle increases to 90 degrees, the incident angle has reached an angle referred to as the Critical Angle. It is expressed as: theta(critical) = sin^-1 (n2/n1)

True or False: Concave mirrors are converging mirrors.

True. Convex mirrors are diverging mirrors. The reverse is true for lenses; concave are diverging, convex are converging.

Why does dispersion occur breaking white light into it's colored components when shown through a prism?

White light diverges as it is refracted through a prism, and breaks into multiple colors because the speed of light as it travels through a medium is different for each wavelength. The lower wavelength the lower the index of refraction, thus the higher the angle bent from normal. When white light (all colors) pass through at once their colors all travel at different wavelengths, and this all bend at different angles.