Slide 1 / 77 Slide 2 / 77 Geometric Optics www.njctl.org Slide 3 / 77 Slide 4 / 77 Table of Contents Click on the topic to go to that section Reflection Reflection · Spherical Mirror · Refraction and Snell's Law · Thin Lenses · Return to Table of Contents Slide 5 / 77 Slide 6 / 77 The Ray Model of Light Reflection Light can travel in straight lines. We represent this using rays, Law of reflection: which are straight lines emanating from a light source or object. This is really an idealization but it is very useful. The angle of incidence is equal to the angle of reflection. Both angles are measured from the line normal to the For instance, you can see a surface. (Remember: Normal means perpendicular.) pencil on a desk from any angle as long as there is Normal to nothing in your way. Light surface reflects off the pencil in all directions, which is Incident ray Reflected ray represented by rays. You Angle of Angle of incidence reflection see the rays that hit your eye. θ i θ r
Slide 7 / 77 Slide 8 / 77 Reflection Reflection With diffuse reflection, your eye sees reflected light at all angles When the light hits a rough surface and reflects, the law of but no image is really formed. With specular reflection (from a reflection still holds but the angle of incidence varies so the mirror) , your eye must be in the correct position. light is diffused. Both eyes see some One eye sees reflected light reflected light. the other does not. Slide 9 / 77 Slide 10 / 77 Reflection 1 The angle of reflection is ________ the angle of incidence. When you look into a plane (or flat) mirror, you see an image which appears to be behind the mirror. This is called a virtual A less than image since the light does not go through it. The distance from B equal to the object to the mirror is the same as the distance from the mirror to the image. C greater than d o d i Slide 11 / 77 Slide 12 / 77 2 An object is placed in front of a plane mirror. Where is the image located? Spherical Mirror C A B D E Object Return to Table of Contents
Slide 13 / 77 Slide 14 / 77 Spherical Mirror Spherical Mirror Spherical Mirrors are shaped like sections of a sphere and may be Rays coming in from a far away object are effectively parallel. reflective on either the inside called concave (where parallel rays reflect and converge) or outside called convex (where parallel rays reflect and diverge). Slide 15 / 77 Slide 16 / 77 Spherical Mirror Spherical Mirror For mirrors with large curvatures, parallel rays do not all converge If the curvature is small, the at exactly the same point. This is called spherical aberration. focus is much more precise. C f The focal point is where the rays converge. r f The focal length of a spherical mirror is half the radius of curvature. Slide 17 / 77 Slide 18 / 77 Spherical Mirror Spherical Mirror We can use ray diagrams to determine where the image will be 1. A ray that is first parallel to the axis and then, after when using a spherical mirror. We draw three principle rays: reflection, passes through the focal point. 1. A ray that is first parallel to the axis and then, after reflection, passes through the focal point. 2. A ray that first passes through the focal point and then, C F after reflection, is parallel to the axis. 3. A ray perpendicular to the mirror and then reflects back on itself. 4. A ray that strikes the mirror at the principal axis (and a certain angle) and reflects back (at the same angle).
Slide 19 / 77 Slide 20 / 77 Spherical Mirror Spherical Mirror 3. A ray perpendicular to the mirror and then reflects back on 2. A ray that first passes through the focal point and then, itself. (Note: this ray always goes through the center of curvature.) after reflection, is parallel to the axis. C F C F Slide 21 / 77 Slide 22 / 77 Spherical Mirror Spherical Mirror 4. A ray that strikes the mirror We can derive an equation that at the principal axis (and a relates the object distance, image certain angle) and reflects distance, and focal length. back (at the same angle). C F C F Really, only two rays are needed to see where the image is located, but it is sometimes good to draw more. Slide 23 / 77 Slide 24 / 77 Spherical Mirror Spherical Mirror We can also derive an equation that This object is between relates the object distance, image the center of curvature distance, and magnification. and the focal point. Its image is magnified, real, and inverted. C F C F The negative sign indicates that the image is inverted. (We do not need to use the negative sign because we can always draw a ray diagram and see if the image is inverted or upright.)
Slide 25 / 77 Slide 26 / 77 Spherical Mirror Spherical Mirror If the object is past the If the object is past the center of curvature... center of curvature... the image is de- magnified, real, and inverted. C F C F Slide 27 / 77 Slide 28 / 77 Spherical Mirror Spherical Mirror If the object is inside the If the object is inside the focal point... focal point... the image is magnified, virtual and upright. C F C F As you can see, if the rays do not intersect in real space, we must extended dotted lines backwards to form a virtual image Slide 29 / 77 Slide 30 / 77 Spherical Mirror Spherical Mirror If the object is in front of the If the object is in front of the convex mirror... convex mirror ... the image is de- magnified, virtual and upright. F C F C
Slide 31 / 77 Slide 32 / 77 3 A ray of light strikes a convex mirror parallel to the central axis. 4 A candle is placed in front of a concave mirror between the center Which of the following represents the reflected ray? of curvature and the focal point. The image is: C B A real, inverted, and magnified. B real, inverted, and demagnified. D C virtual, upright, and magnified. A D virtual, upright, and demagnified. F C E real, upright, and magnified. E Slide 33 / 77 Slide 34 / 77 5 A candle with a height of 6 cm is placed 21 cm in front of a 6 A candle with a height 6 cm is placed 21 cm in front of a concave concave mirror with a focal length of 7 cm. How far is the image mirror with a focal length of 7 cm. How tall is the image? from the mirror? Slide 35 / 77 Slide 36 / 77 7 Which of the following indicates the image distance, d i , for an object that is placed in front of a concave mirror if the image created is inverted? Select two answers. Refraction and A d o = f Snell's Law B 2f > d o > f C d o > 2f D f > d o Return to Table of Contents
Slide 37 / 77 Slide 38 / 77 Refraction and Snell's Law Refraction and Snell's Law Light also changes direction when it enters a new medium. This is As we saw in called refraction. The angle of incidence is related to the angle of Electromagnetic Waves, refraction. When the ray goes from less dense to more dense, it light slows when traveling bends towards the normal line and the refracted angle is smaller. through a medium. The When the ray goes from more dense to less dense, it bends away index of refraction (n) of the from the normal line and the refracted angle is larger. medium is the ratio of Refracted Normal Normal Incident the speed of light in Reflected ray line line ray ray vacuum to the speed of light in the medium: # 2 # 1 Air (n 1 ) Air (n 2 ) Water (n 2 ) Water (n 1 ) Refracted ray # 1 # 2 Reflected Incident ray ray Slide 39 / 77 Slide 40 / 77 Refraction and Snell's Law Refraction and Snell's Law Incident When light passes from air ray Glass (n 2 ) Air (n 1 ) to a different medium back n 1 sin # 1 = n 2 sin # 2 to air the ray that enters the medium is parallel to # 1 the ray that exits the medium. Refracted # 2 Normal Normal Incident Reflected ray line line ray ray Using geometry, we can # 2 find the liner displacement # 1 # 2 # 1 between the emerging ray Air (n 2 ) Air (n 1 ) Emerging and the incident ray, if we ray Water (n 2 ) Water (n 1 ) know the angle of the Incident incident ray and the ray Refracted thickness of the other Linear ray # 1 # 2 Reflected Incident displacement medium. ray ray Slide 41 / 77 Slide 42 / 77 Refraction and Snell's Law Refraction and Snell's Law If the incident angle is just big enough, the refracted ray will be This is why objects look weird if they are partially under water. parallel to the surface, so the refracted angle will be 90 o . This angel is called the critical angle. Normal line Refracted # 2 ray Air (n 2 ) Water (n 1 ) # 1 Incident ray
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