Reflection and Mirrors Refraction and Lenses

The Law of Reflection “ The angle of incidence equals the angle of reflection.”

The Law of Reflection When light strikes a surface it is reflected. The light ray striking the surface is called the incident ray. A normal (perpendicular) line is then drawn at the point where the light strikes the surface. The angle between the incident ray and the normal is called the angle of incidence. The light is then reflected so that the angle of incidence is equal to the angle of reflection. The angle of reflection is the angle between the normal and the reflected light ray.

Normal Angle of Incidence Angle of Reflection Incident Ray Reflected Ray Mirror

The incident ray, normal, and reflected ray are all in the same plane.

Regular reflection occurs when light is reflected from a smooth surface. When parallel light rays strike a smooth surface they are reflected and will still be parallel to each other.

Diffuse reflection occurs when light is reflected from a rough surface Diffuse reflection occurs when light is reflected from a rough surface. The word rough is a relative term. The surface is rough at a microscopic level. For example, an egg is a rough surface. When parallel light rays strike a rough surface, the light rays are reflected in all directions according to the law of reflection.

Types of Mirrors Convex Concave Convex mirrors are made from a section of a sphere whose outer surface was reflective. Convex mirrors are also known as diverging mirrors since they spread out light rays. They are typically found as store security mirrors. Concave mirrors are made from a section of a sphere whose inner surface was reflective. Concave mirrors are also known as converging mirrors since they bring light rays to a focus. They are typically found as magnifying mirrors Concave

Plane Mirrors have a flat surface Plane Mirrors have a flat surface. The mirror hanging on the wall in your bathroom is a plane mirror.

Real images are images that form where light rays actually cross. In the case of mirrors, that means they form on the same side of the mirror as the object since light can not pass through a mirror. Real images are always inverted (flipped upside down). Virtual images are images that form where light rays appear to have crossed. In the case of mirrors, that means they form behind the mirror. Virtual images are always upright.

Plane Mirror In a plane mirror the object is the same size, upright, and the same distance behind the mirror as the object is in front of the mirror.

Images in a plane mirror are also reversed left to right.

Curved Mirrors The center of curvature also known as radius of curvature (C) of a curved mirror is located at the center of the sphere from which it was made. The focal point (f) is located halfway between the mirror’s surface and the center of curvature. C = 2f The principle axis is a line that passes through both the center of curvature (C) and the focal point (f) and intersects the mirror at a right angle.

Concave Mirrors Convex Mirrors f C Principle Axis Concave Mirrors Light source Convex Mirrors f C Principle Axis Light source

Rules for Locating Reflected Images 1. Light rays that travel through the center of curvature (C) strike the mirror and are reflected back along the same path. 2. Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f). 3. Light rays that travel through the focal point (f), strike the mirror, and are reflected back parallel to the principle axis.

All three of these light rays will intersect at the same point if they are drawn carefully. However, the image can be located by finding the intersection of any two of these light rays.

Locating images in concave mirrors

Concave Mirror with the Object located beyond C

Concave Mirror Object beyond C Light rays that travel through the center of curvature (C) hit the mirror and are reflected back along the same path.

Concave Mirror Object beyond C Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f).

Concave Mirror Object beyond C Light rays that travel through the focal point (f), strike the mirror, and are reflected back parallel to the principle axis.

Concave Mirror Object beyond C Image: Real Inverted Smaller Between f and C The image is located where the reflected light rays intersect

Concave Mirror with the Object located at C

Concave Mirror Object at C Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f).

Concave Mirror Object at C Light rays that travel through the focal point (f), strike the mirror, and are reflected back parallel to the principle axis.

Concave Mirror Object at C Image: Real Inverted Same Size At C The image is located where the reflected light rays intersect

Concave Mirror with the Object located between f and C

Concave Mirror Object between f and C f C Light rays that travel through the center of curvature (C) hit the mirror and are reflected back along the same path.

Concave Mirror Object between f and C f C Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f).

Concave Mirror Object between f and C f C Light rays that travel through the focal point (f), strike the mirror, and are reflected back parallel to the principle axis.

The image is located where the reflected light rays intersect Concave Mirror Object between f and C Image: Real Inverted Larger Beyond C f C The image is located where the reflected light rays intersect

Concave Mirror with the Object located at f

Concave Mirror Object at f Light rays that pass through the center of curvature hit the mirror and are reflected back along the same path.

Concave Mirror Object at f Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f).

Concave Mirror Object at f No image is formed. All reflected light rays are parallel and do not cross

Solar "Death Ray": http://www.youtube.com/watch?v=TtzRAjW6KO0

Concave Mirror with the Object located between f and the mirror

Concave Mirror Object between f and the mirror Light rays that travel through the center of curvature (C) hit the mirror and are reflected back along the same path.

Concave Mirror Object between f and the mirror Light rays that travel through the focal point (f), strike the mirror, and are reflected back parallel to the principle axis.

Concave Mirror Object between f and the mirror Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f).

Concave Mirror Object between f and the mirror Image: Virtual Upright Larger Further away The image is located where the reflected light rays intersect

Locating images in convex mirrors

Convex Mirror with the Object located anywhere in front of the mirror

Convex Mirror Object located anywhere f C Light rays that travel through the center of curvature (C) hit the mirror and are reflected back along the same path.

Convex Mirror Object located anywhere f C Light rays that travel parallel to the principle axis, strike the mirror, and are reflected back through the focal point (f).

Convex Mirror Object located anywhere f C Light rays that travel through (toward) the focal point (f), strike the mirror, and are reflected back parallel to the principle axis.

Convex Mirror Object located anywhere f C Image: Virtual Upright Smaller Behind mirror, inside f The image is located where the reflected light rays intersect

Refraction and Lenses

Refraction is the bending of light as it moves from one medium to a medium with a different optical density. This bending occurs as a result of the speed of light changing at the interface between the two media.

Refraction Notice the spoon appears to bend where it enters the water.

The light ray that hits the interface is called the incident ray. At the point where the incident ray hits the interface, a normal (perpendicular) to the surface should be drawn. The angle between the incident ray and the normal is called the angle of incidence. The light ray that passes into the new medium is called the refracted ray. The angle between the refracted ray and the normal is called the angle of refraction.

Angle of Incidence Incident Ray Normal Refracted Ray Angle of Refraction Interface between 2 media

As light strikes the interface between two media with different optical densities at an oblique (not 90o) angle, it changes speed and is refracted. As it moves from a less dense medium to a more dense medium, it bends toward the normal (perpendicular to the interface) and slows down. Less More

As it moves from a more dense medium to a less dense medium, it bends away from the normal and speeds up. Less More

If the light strikes the interface at a 90o angle, it is not refracted and continues moving in a straight line but its speed will change.

When light passes through a parallel sided glass figure, the emergent ray will be parallel to the incident ray because the amount it is bent toward the normal as it enters the glass is the same amount it bends away from the normal as it leaves the glass.

Incident Ray Refracted Ray Normal Normal Emergent Ray glass air

Light rays that strike the parallel sided glass figure perpendicular to the side will pass straight through the piece of glass without bending.

Light is also refracted by the same rules when it goes through an object that does not have parallel sides. However, in this case, the emergent ray will not be parallel to the incident ray. As the light ray enters the prism, it is moving from a less dense to a more dense substance so it is bent toward the normal. As the light ray leaves the prism, it is moving from a more dense to a less dense substance so it is bent away from the normal.

In the picture shown below, the light source is on the right side In the picture shown below, the light source is on the right side. Notice the bending as the light travels through the prism, when it leaves the prism the white light has been separated into its component colors. This separation is due to the fact that each different wave length of light moves at a slightly different speed in glass and is therefore refracted at slightly different amounts.

We are able to see most objects not because they are emitting light but because they reflect light. When you are looking into a pond, at many angles you are able to see the fish below the water but he is not exactly where you appear to see him. Image Object

When light is reflected from a fish and it hits the surface of the water at an angle greater than the critical angle all of the light is reflected back into the water and none is allowed to escape. This is called internal reflection.

Fiber Optic Cables Light is transmitted along a fiber optic cable due to the phenomenon of total internal reflection.

The most common application of refraction in science and technology is lenses. The kind of lenses we typically think of are made of glass. The basic rules of refraction still apply but due to the curved surface of the lenses, they create images.

Types of Lenses Convex lenses are also known as converging lenses since they bring light rays to a focus. Concave lenses are also known as diverging lenses since they spread out light rays.

Parts of a Lens All lenses have a focal point (f). In a convex lens, parallel light rays all come together at a single point called the focal point. In a concave lens, parallel light rays are spread apart but if they are traced backwards, the refracted rays appear to have come from a single point called the focal point. f f

The distance from the lens to the focal point is called the focal length. Typically, a point is also noted that is 2 focal lengths from the lens and is labeled 2f. The principle axis is a line which connects the focal point and the 2f point and intersects the lens perpendicular to its surface. Concave Lens Convex Lens Principle axis Principle axis f 2f f 2f

Concave Lenses aren’t on STAAR, they won’t be on our test and can be omitted from homework assignments.

Rules for Locating Refracted Images 1. Light rays that travel through the center of the lens (where the principle axis intersects the midline) are not refracted and continues along the same path. 2. Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f). 3. Light rays that travel through the focal point (f), strike the lens, and are refracted parallel to the principle axis.

All three of these light rays will intersect at the same point if they are drawn carefully. However, the image can be located by finding the intersection of any two of these light rays.

Real images are images that form where light rays actually cross. In the case of lenses, that means they form on the opposite side of the lens from the object since light can pass through a lens. Real images are always inverted (flipped upside down). Virtual images are images that form where light rays appear to have crossed. In the case of lenses, that means they form on the same side of the lens as the object. Virtual images are always upright.

Images formed by Convex lenses

Locating images in convex lenses

Convex Lenses with the Object located beyond 2f

Convex Lens Object located beyond 2f 2f 2f f f Light rays that travel through the center of the lens are not refracted and continue along the same path.

Convex Lens Object located beyond 2f 2f 2f f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

Convex Lens Object located beyond 2f 2f Image: Real Inverted Smaller Between f and 2f 2f f f The image is located where the refracted light rays intersect

Convex Lenses with the Object located at 2f

Convex Lens Object located at 2f 2f 2f f f Light rays that travel through the center of the lens are not refracted and continue along the same path.

Convex Lens Object located at 2f 2f 2f f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

Convex Lens Object located at 2f 2f Image: Real Inverted Same Size At 2f 2f f f The image is located where the refracted light rays intersect

Convex Lenses with the Object located between f and 2f

Convex Lens Object located between f and 2f 2f 2f f f Light rays that travel through the center of the lens are not refracted and continue along the same path.

Convex Lens Object located between f and 2f 2f 2f f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

Convex Lens Object located between f and 2f 2f Image: Real Inverted Larger Beyond 2f 2f f f The image is located where the refracted light rays intersect

Convex Lenses with the Object located at f

Convex Lens Object located at f 2f 2f f f Light rays that travel through the center of the lens are not refracted and continue along the same path.

Convex Lens Object located at f 2f 2f f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

Convex Lens Object located at f 2f 2f f f No image is formed. All refracted light rays are parallel and do not cross

Convex Lenses with the Object located between f and the lens

Convex Lens Object located between f and the lens f 2f Light rays that travel through the center of the lens are not refracted and continue along the same path.

Convex Lens Object located between f and the lens f 2f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

Convex Lens Object located between f and the lens 2f 2f f f These two refracted rays do not cross to the right of the lens so we have to project them back behind the lens.

Object located between f and the lens Convex Lens Object located between f and the lens 2f Image: Virtual Upright Larger Further away 2f f f The image is located at the point which the refracted rays APPEAR to have crossed behind the lens

The Lens Formula

Object distance do Image distance di Focal length f

Sign Conventions: 1. All distances are measured from center of optical device 2. Distances of real objects and images are positive " virtual " " negative (example of a virtual object?) 3. Heights of object and images are positive when upright and negative when inverted. 4. Focal lengths of converging(convex) lenses are positive; diverging lenses have negative focal lengths.

do di f

Sample Problem p.575

Di=

p. 576 problems 1,2 and 3 just find di, not magnification

The eye contains a convex lens The eye contains a convex lens. This lens focuses images on the back wall of the eye known as the retina.

The distance from the lens to the retina is fixed by the size of the eyeball. For an object at a given distance from the eye, the image is in focus on the retina. Although the image on the retina is inverted, the brain interprets the impulses to give an erect mental image.

If the object moved closer to the eye and nothing else changed the image would move behind the retina the image would therefore appear blurred. Similarly if the object moved away from the eye the image would move in front of the retina again appearing blurred. To keep an object in focus on the retina the eye lens can be made to change thickness. This is done by contracting or extending the eye muscles. We make our lenses thicker to focus on near objects and thinner to focus on far objects.

Someone who is nearsighted can see near objects more clearly than far objects. The retina is too far from the lens and the eye muscles are unable to make the lens thin enough to compensate for this. Diverging glass lenses are used to extend the effective focal length of the eye lens.

Someone who is farsighted can see far objects more clearly than near objects. The retina is now too close to the lens. The lens would have to be considerable thickened to make up for this. A converging glass lens is used to shorten the effective focal length of the eye lens. Today’s corrective lenses are carefully ground to help the individual eye but cruder lenses for many purposes were made for 300 years before the refractive behavior of light was fully understood.