Reflection and Refraction of Light From “College Physics” Serway and Faughn with modifications

Reflection of Light A ray of light, the incident ray, travels in a medium A ray of light, the incident ray, travels in a medium When it encounters a boundary with a second medium, part of the incident ray is reflected back into the first medium When it encounters a boundary with a second medium, part of the incident ray is reflected back into the first medium This means it is directed backward into the first medium This means it is directed backward into the first medium

Specular Reflection Specular reflection is reflection from a smooth surface Specular reflection is reflection from a smooth surface The reflected rays are parallel to each other The reflected rays are parallel to each other All reflection in this text is assumed to be specular All reflection in this text is assumed to be specular

Diffuse Reflection Diffuse reflection is reflection from a rough surface Diffuse reflection is reflection from a rough surface The reflected rays travel in a variety of directions The reflected rays travel in a variety of directions Diffuse reflection makes the road easy to see at night Diffuse reflection makes the road easy to see at night

QUICK QUIZ 22.1 Which part of the figure below shows specular reflection of light from the roadway?

QUICK QUIZ 22.1 ANSWER (a). In part (a), you can see clear reflections of the headlights and the lights on the top of the truck. The reflection is specular. In part (b), although bright areas appear on the roadway in front of the headlights, the reflection is not as clear and no separate reflection of the lights from the top of the truck is visible. The reflection in part (b) is mostly diffuse.

Law of Reflection The normal is a line perpendicular to the surface The normal is a line perpendicular to the surface It is at the point where the incident ray strikes the surface It is at the point where the incident ray strikes the surface The incident ray makes an angle of θ 1 with the normal The incident ray makes an angle of θ 1 with the normal The reflected ray makes an angle of θ 1 ’ with the normal The reflected ray makes an angle of θ 1 ’ with the normal

Law of Reflection, cont The angle of reflection is equal to the angle of incidence The angle of reflection is equal to the angle of incidence θ 1 = θ 1 ’ θ 1 = θ 1 ’

Mirrors and Lenses

Notation for Mirrors and Lenses The object distance is the distance from the object to the mirror or lens The object distance is the distance from the object to the mirror or lens Denoted by p Denoted by p The image distance is the distance from the image to the mirror or lens The image distance is the distance from the image to the mirror or lens Denoted by q Denoted by q The lateral magnification of the mirror or lens is the ratio of the image height to the object height The lateral magnification of the mirror or lens is the ratio of the image height to the object height Denoted by M Denoted by M

Types of Images for Mirrors and Lenses A real image is one in which light actually passes through the image point A real image is one in which light actually passes through the image point Real images can be displayed on screens Real images can be displayed on screens A virtual image is one in which the light does not pass through the image point A virtual image is one in which the light does not pass through the image point The light appears to diverge from that point The light appears to diverge from that point Virtual images cannot be displayed on screens Virtual images cannot be displayed on screens

More About Images To find where an image is formed, it is always necessary to follow at least two rays of light as they reflect from the mirror To find where an image is formed, it is always necessary to follow at least two rays of light as they reflect from the mirror

Flat Mirror Simplest possible mirror Simplest possible mirror Properties of the image can be determined by geometry Properties of the image can be determined by geometry One ray starts at P, follows path PQ and reflects back on itself One ray starts at P, follows path PQ and reflects back on itself A second ray follows path PR and reflects according to the Law of Reflection A second ray follows path PR and reflects according to the Law of Reflection

Properties of the Image Formed by a Flat Mirror The image is as far behind the mirror as the object is in front The image is as far behind the mirror as the object is in front q = p q = p The image is unmagnified The image is unmagnified The image height is the same as the object height The image height is the same as the object height h’ = h and M = 1 h’ = h and M = 1 The image is virtual The image is virtual The image is upright The image is upright It has the same orientation as the object It has the same orientation as the object There is an apparent left-right reversal in the image There is an apparent left-right reversal in the image

Spherical Mirrors A spherical mirror has the shape of a segment of a sphere A spherical mirror has the shape of a segment of a sphere A concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of the curve A concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of the curve A convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the curve A convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the curve

Focal Length If an object is very far away then the incoming rays are essentially parallel If an object is very far away then the incoming rays are essentially parallel In this special case, the image point is called the focal point In this special case, the image point is called the focal point The distance from the mirror to the focal point is called the focal length The distance from the mirror to the focal point is called the focal length The focal length is ½ the radius of curvature The focal length is ½ the radius of curvature

Focal Length Shown by Parallel Rays

Convex Mirrors A convex mirror is sometimes called a diverging mirror A convex mirror is sometimes called a diverging mirror The rays from any point on the object diverge after reflection as though they were coming from some point behind the mirror The rays from any point on the object diverge after reflection as though they were coming from some point behind the mirror The image is virtual because it lies behind the mirror at the point where the reflected rays appear to originate The image is virtual because it lies behind the mirror at the point where the reflected rays appear to originate In general, the image formed by a convex mirror is upright, virtual, and smaller than the object In general, the image formed by a convex mirror is upright, virtual, and smaller than the object

Refraction of Light When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium The ray that enters the second medium is bent at the boundary The ray that enters the second medium is bent at the boundary This bending of the ray is called refraction This bending of the ray is called refraction

Refraction of Light, cont The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane The angle of refraction, θ 2, depends on the properties of the medium The angle of refraction, θ 2, depends on the properties of the medium

Following the Reflected and Refracted Rays Ray  is the incident ray Ray  is the incident ray Ray  is the reflected ray Ray  is the reflected ray Ray is refracted into the lucite Ray is refracted into the lucite Ray  is internally reflected in the lucite Ray  is internally reflected in the lucite Ray is refracted as it enters the air from the lucite Ray is refracted as it enters the air from the lucite

More About Refraction The angle of refraction depends upon the material and the angle of incidence The angle of refraction depends upon the material and the angle of incidence The path of the light through the refracting surface is reversible The path of the light through the refracting surface is reversible

QUICK QUIZ 22.2 If beam 1 is the incoming beam in the figure below, which of the other four beams are reflected and which are refracted?

QUICK QUIZ 22.2 ANSWER Beams 2 and 4 are reflected; beams 3 and 5 are refracted.

Refraction Details, 1 Light may refract into a material where its speed is lower Light may refract into a material where its speed is lower The angle of refraction is less than the angle of incidence The angle of refraction is less than the angle of incidence The ray bends toward the normal The ray bends toward the normal

Refraction Details, 2 Light may refract into a material where its speed is higher Light may refract into a material where its speed is higher The angle of refraction is greater than the angle of incidence The angle of refraction is greater than the angle of incidence The ray bends away from the normal The ray bends away from the normal

Frequency Between Media As light travels from one medium to another, its frequency does not change As light travels from one medium to another, its frequency does not change Both the wave speed and the wavelength do change Both the wave speed and the wavelength do change The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same

The amount of transmission and reflection depends upon the difference in the “density” of the 2 media. i.e the bigger the difference, the greater the amount of reflection.

Refraction through a glass block: Wave slows down and bends towards the normal due to entering a more dense medium Wave speeds up and bends away from the normal due to entering a less dense medium Wave slows down but is not bent, due to entering along the normal

Refraction in a Prism The amount the ray is bent away from its original direction is called the angle of deviation, δ The amount the ray is bent away from its original direction is called the angle of deviation, δ Since all the colors have different angles of deviation, they will spread out into a spectrum Since all the colors have different angles of deviation, they will spread out into a spectrum Violet deviates the most Violet deviates the most Red deviates the least Red deviates the least

The Rainbow A ray of light strikes a drop of water in the atmosphere A ray of light strikes a drop of water in the atmosphere It undergoes both reflection and refraction It undergoes both reflection and refraction First refraction at the front of the drop First refraction at the front of the drop Violet light will deviate the most Violet light will deviate the most Red light will deviate the least Red light will deviate the least

The Rainbow, 2 At the back surface the light is reflected At the back surface the light is reflected It is refracted again as it returns to the front surface and moves into the air It is refracted again as it returns to the front surface and moves into the air The rays leave the drop at various angles The rays leave the drop at various angles The angle between the white light and the violet ray is 40° The angle between the white light and the violet ray is 40° The angle between the white light and the red ray is 42° The angle between the white light and the red ray is 42°

Observing the Rainbow If a raindrop high in the sky is observed, the red ray is seen A drop lower in the sky would direct violet light to the observer The other colors of the spectra lie in between the red and the violet

Total Internal Reflection Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction Ray 5 shows internal reflection Ray 5 shows internal reflection

Critical Angle A particular angle of incidence will result in an angle of refraction of 90° A particular angle of incidence will result in an angle of refraction of 90° This angle of incidence is called the critical angle This angle of incidence is called the critical angle

Critical Angle, cont For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary This ray obeys the Law of Reflection at the boundary This ray obeys the Law of Reflection at the boundary Total internal reflection occurs only when light attempts to move from a medium of higher optical density to a medium of lower optical density Total internal reflection occurs only when light attempts to move from a medium of higher optical density to a medium of lower optical density

Finding the Critical Angle… 1) Ray gets refracted 4) Ray gets internally reflected 3) Ray still gets refracted (just!) 2) Ray still gets refracted THE CRITICAL ANGLE

Optical fibres

Fiber Optics An application of internal reflection An application of internal reflection Plastic or glass rods are used to “pipe” light from one place to another Plastic or glass rods are used to “pipe” light from one place to another Applications include Applications include medical use of fiber optic cables for diagnosis and correction of medical problems medical use of fiber optic cables for diagnosis and correction of medical problems Telecommunications Telecommunications

Thin Lenses A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane Lenses are commonly used to form images by refraction in optical instruments Lenses are commonly used to form images by refraction in optical instruments

Thin Lens Shapes These are examples of converging lenses These are examples of converging lenses They have positive focal lengths They have positive focal lengths They are thickest in the middle They are thickest in the middle

More Thin Lens Shapes These are examples of diverging lenses These are examples of diverging lenses They have negative focal lengths They have negative focal lengths They are thickest at the edges They are thickest at the edges

Focal Length of Lenses The focal length, ƒ, is the image distance that corresponds to an infinite object distance The focal length, ƒ, is the image distance that corresponds to an infinite object distance This is the same as for mirrors This is the same as for mirrors A thin lens has two focal points, corresponding to parallel rays from the left and from the right A thin lens has two focal points, corresponding to parallel rays from the left and from the right A thin lens is one in which the distance between the surface of the lens and the center of the lens is negligible A thin lens is one in which the distance between the surface of the lens and the center of the lens is negligible

Focal Length of a Converging Lens The parallel rays pass through the lens and converge at the focal point The parallel rays can come from the left or right of the lens

Focal Length of a Diverging Lens The parallel rays diverge after passing through the diverging lens The focal point is the point where the rays appear to have originated

Ray Diagrams for Thin Lenses Ray diagrams are essential for understanding the overall image formation Ray diagrams are essential for understanding the overall image formation Three rays are drawn Three rays are drawn The first ray is drawn parallel to the first principle axis and then passes through (or appears to come from) one of the focal lengths The first ray is drawn parallel to the first principle axis and then passes through (or appears to come from) one of the focal lengths The second ray is drawn through the center of the lens and continues in a straight line The second ray is drawn through the center of the lens and continues in a straight line The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axis The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axis There are an infinite number of rays, these are convenient There are an infinite number of rays, these are convenient

Ray Diagram for Converging Lens, p > f The image is real The image is inverted

Ray Diagram for Converging Lens, p < f The image is virtual The image is upright

Ray Diagram for Diverging Lens The image is virtual The image is upright