Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror 1.First ray goes parallel to the mirror and then reflects back down through the focus. 2.Second Ray goes through the focus and into the mirror and then reflected back parallel to axis. 3.Ray drawn to center of lens and reflects back downwards at an equal angle (symmetric) 4.If at or within the focal length you an draw a line perpendicular to the mirror so that it goes back through itself and into the center of curvature (R = 2f). This can replace the second ray above which now cannot be drawn.

Concave Mirror FC Rule 1 First ray goes parallel to the mirror and then reflects back down through the focus.

Concave Mirror FC Ray 1 Ray 2 Second Ray goes through the focus and into the mirror and then reflected back parallel to axis.

Concave Mirror FC Ray drawn to center of lens and reflects back downwards at an equal angle (symmetric) Ray 1 Ray 2 Ray 3

Concave Mirror Lets draw ray diagrams for the following cases: do = f f<do<R do>R do>f do=R

Concave Mirror Object is on the Focal Point Do = F

Concave Mirror FC

FC d o = f

Concave Mirror FC d o = f

Concave Mirror FC d o = f

Concave Mirror FC d o = f Ray 1

Concave Mirror FC d o = f Ray 1 Cannot Draw 2nd ray from Object through focus.

Concave Mirror FC d o = f Ray 1 Cannot Draw 2nd ray from Object through focus. Ray 3

Concave Mirror FC d o = f Ray 1 Cannot Draw 2nd ray from Object through focus. Ray 3 They do not Cross: No Image!

Concave Mirror FC d o = f Ray 1 Cannot Draw 2nd ray from Object through focus. Ray 3 They do not Cross: No Image! Even a fourth ray will not cross the others. Ray 4

Concave Mirror Object is Between Focal Point and Center of Curvature f<do<R

Concave Mirror FC f<do<R

Concave Mirror FC f<do<R Ray 1

Concave Mirror FC f<do<R Ray 1 Ray 2

Concave Mirror FC f<do<R Ray 1 Ray 2 Ray 3

Concave Mirror FC f<do<R Ray 1 Ray 2 Ray 3 Real Image: Magnified

Concave Mirror Object distance is Greater than or outside the radius of curvature (C) do>R

Concave Mirror FC do>R

Concave Mirror FC do>R Ray 1

Concave Mirror FC do>R Ray 1 Ray 2

Concave Mirror FC do>R Ray 1 Ray 2 Ray 3

Concave Mirror FC do>R Ray 1 Ray 2 Ray 3 Image Real and Demagnified

Concave Mirror Object distance is smaller than or within the radius of curvature (C) do<f

Concave Mirror FC do<f

Concave Mirror FC do<f Ray 1

Concave Mirror FC do<f Ray 1 Ray 2

Concave Mirror FC do<f Ray 1 Ray 2 Ray 3

Is there an Image? What do you think?

Concave Mirror FC do<f Ray 1 Ray 2 Ray 3

Concave Mirror FC do<f Ray 1 Ray 2 Ray 3

Concave Mirror FC do<f Ray 1 Ray 2 Ray 3

Concave Mirror FC do<f Ray 1 Ray 2 Ray 3 Image is Virtual, Right side up and Magnified

Compare this to the First Example with no Image. Why Didn’t that one have a virtual image?

Concave Mirror FC d o = f Ray 1 Ray 2 Cannot Draw 3rd ray from Object through focus. Ray 4

The Rays appear to be pretty much parallel. Therefore they will not cross on either side so there is no image, virtual or real.

Concave Mirror Object distance is equal to radius of curvature do = R

Concave Mirror FC d o = R

Concave Mirror FC d o = R

Concave Mirror FC d o = R Ray 1

Concave Mirror FC d o = R Ray 1

Concave Mirror FC d o = R Ray 1 Ray 2

Concave Mirror FC d o = R Ray 1 Ray 2

Concave Mirror FC d o = R Ray 1 Ray 2 Ray 3

Concave Mirror FC d o = R Ray 1 Ray 2 Ray 3

Concave Mirror FC d o = R Ray 1 Ray 2 Ray 3 Image is Real, upside down and demagnified.

Cosmetics This is a cosmetics mirror. Up close (do <f) you are right side up and appear magnified. As you move away your image will eventually invert and become smaller.

Convex Mirror 1.First ray goes parallel to the mirror and then reflects back up (dotted image line goes through focus on the other side). 2.Second Ray is aimed directly at the center of curvature on the other side but once it hits the mirror it reflects back through itself with the dotted image line going through C). 3.Ray drawn aimed at focus on the other side and reflect off the mirror parallel to the axis (dotted line drawn parallel in the other direction)

Convex Mirror We shall now draw Convex Mirror Diagrams for the following cases: do>R f R do<f

Convex Mirror Distance to Object is greater than radius of curvature do > R

Convex Mirror FC

FC do>R

Convex Mirror FC do>R

Convex Mirror FC do>R

Convex Mirror FC do>R Ray 1

Convex Mirror FC do>R Ray 1

Convex Mirror FC do>R Ray 1

Convex Mirror FC do>R Ray 1

Convex Mirror FC do>R Ray 1 Ray 2

Convex Mirror FC do>R Ray 1 Ray 2

Convex Mirror FC do>R Ray 1 Ray 2

Convex Mirror FC do>R Ray 1 Ray 2 Ray 3

Convex Mirror FC do>R Ray 1 Ray 2 Ray 3

Convex Mirror FC do>R Ray 1 Ray 2 Ray 3 Image Virtual, Right Side up Demagnified

Convex Mirror Distance to Object is in between focus and radius of curvature. f<do<R

Convex Mirror FC F<do<R

Convex Mirror FC F<do<R

Convex Mirror FC F<do<R

Convex Mirror FC F<do<R

Convex Mirror FC F<do<R Ray 1

Convex Mirror FC F<do<R Ray 1

Convex Mirror FC F<do<R Ray 1

Convex Mirror FC F<do<R Ray 1 Ray 2

Convex Mirror FC F<do<R Ray 1 Ray 2

Convex Mirror FC F<do<R Ray 1 Ray 2

Convex Mirror FC F<do<R Ray 1 Ray 2

Convex Mirror FC F<do<R Ray 1 Ray 2 Ray 3

Convex Mirror FC F<do<R Ray 1 Ray 2 Ray 3

Convex Mirror FC F<do<R Ray 1 Ray 2 Ray 3

Convex Mirror FC f<do<R Ray 1 Ray 2 Ray 3 Image: Virtual, right side up, demagnified.

Convex Mirror Distance to Object less than the distance to the focus do<f

Convex Mirror FC do<f

Convex Mirror FC do<f

Convex Mirror FC do<f

Convex Mirror FC do<f

Convex Mirror FC do<f

Convex Mirror FC do<f Ray 1

Convex Mirror FC do<f Ray 1

Convex Mirror FC do<f Ray 1

Convex Mirror FC do<f Ray 1

Convex Mirror FC do<f Ray 1 Ray 2

Convex Mirror FC do<f Ray 1 Ray 2

Convex Mirror FC do<f Ray 1 Ray 2

Convex Mirror FC do<f Ray 1 Ray 2 Ray 3

Convex Mirror FC do<f Ray 1 Ray 2 Ray 3

Convex Mirror FC do<f Ray 1 Ray 2 Ray 3

Convex Mirror FC do<f Ray 1 Ray 2 Ray 3 Image Virtual, right side up, demagnified

Convex or Converging Lens For the Following Conditions do=f f 2f do<f do=2f Note the lens thickness is to be assumed small so that refraction is not a concern.

Convex Lens Rules First ray is drawn parallel to principal axis until it strikes the center of the mirror. It then converged down on through the focal point on the other side of the lens. The second ray has a straight line drawn from the object to the focus to the lens on the same side and then it refracts parallel to the principal axis on the other side. The third ray is usually drawn in a direction from the object through the center of the lens itself into the other side.

Convex or Converging Lens FF Ray 1 First ray is drawn parallel to principal axis until it strikes the center of the mirror. It then converged down on through the focal point on the other side of the lens

Convex or Converging Lens FF Ray 1 Ray 2 The second ray has a straight line drawn from the object to the focus to the lens on the same side and then it refracts parallel to the principal axis on the other side.

Convex or Converging Lens FF Ray 1 Ray 2 Ray 3 The third ray is usually drawn in a direction from the object through the center of the lens itself into the other side.

Convex or Converging Lens Distance to Object is in between focus and radius of curvature. do=f

Convex or Converging Lens FF do=f

Convex or Converging Lens FF do=f

Convex or Converging Lens FF do=f

Convex or Converging Lens FF do=f Ray 1

Convex or Converging Lens FF do=f Ray 1 Ray 2

Convex or Converging Lens FF do=f Ray 1 Ray 2 Cannot Draw Ray Three Through Focus as the object is on the focus.

Convex or Converging Lens FF do=f Ray 1 Ray 2 Cannot Draw Ray Three Through Focus as the object is on the focus. No Image!

Convex or Converging Lens FF f<do<2f

Convex or Converging Lens FF f<do<2f

Convex or Converging Lens FF f<do<2f Ray 1

Convex or Converging Lens FF f<do<2f Ray 1 Ray 2

Convex or Converging Lens FF f<do<2f Ray 1 Ray 2 Ray 3

Convex or Converging Lens FF f<do<2f Ray 1 Ray 2 Ray 3

Convex or Converging Lens FF f<do<2f Ray 1 Ray 2 Ray 3 Real Image, Inverted and Magnified

Convex or Converging Lens FF do>2f

Convex or Converging Lens FF do>2f Ray 1 Ray 2

Convex or Converging Lens FF do>2f Ray 1 Ray 2 Ray 3

Convex or Converging Lens FF do>2f Ray 1 Ray 2 Ray 3 Image is Real Upside Down Demagnified

Convex or Converging Lens FF do<f

Convex or Converging Lens FF do<f Ray 1

Convex or Converging Lens FF do<f Ray 1 Ray 2

Convex or Converging Lens FF do<f Ray 1 Ray 2 Cannot Draw Ray 3 but there is an image still!

Convex or Converging Lens FF do<f Ray 1 Ray 2 Cannot Draw Ray 3 but there is an image still!

Convex or Converging Lens FF do<f Ray 1 Ray 2 Cannot Draw Ray 3 but there is an image still!

Convex or Converging Lens FF do<f Ray 1 Ray 2 Image is Virtual Upside Down and really magnified

Convex or Converging Lens FF do=2f

Convex or Converging Lens FF do=2f Ray 1

Convex or Converging Lens FF do=2f Ray 1 Ray 2

Convex or Converging Lens FF do=2f Ray 1 Ray 2 Ray 3

Convex or Converging Lens FF do=2f Ray 1 Ray 2 Ray 3 Image Real Upside Down Magnified

Magnifying Glass This double convex lens is how a magnifying glass works. When at the focus (do=f) there is no image (very blurry). When close (do<f) it magnifies an image which appears normal (right side up). As you move farther the image will appear to be upside down buy magnified. As you move even farther the image will stay inverted but get smaller. Try it out next time you have a magnifying glass!!!!

Concave or Diverging Lens For the Following Conditions do=f f 2f do<f Note the lens thickness is to be assumed small so that refraction is not a concern.

Rules for Concave Lenses 1 st ray is drawn parallel to principle axis and hits the lens. It will refract upwards with its reversibility going through the focal point on the same side. 2 nd ray is drawn from the object in a direction diagonal to the focal point on the other side but goes parallel to the principal axis once it crossed the lens. 3 rd ray is drawn from the object straight through the center of the lens.

Concave or Diverging Lens FF Ray 1 Rule One : Parallel to axis once it hits lens. Goes diagonally upwards with reversisibility going through focus on same side.

Concave or Diverging Lens FF Ray 1 Ray 2 Rule Two : Toward focus on other side but parallel to axis once it hits lens.

Concave or Diverging Lens FF Ray 1 Ray 2 Ray 3 Rule Three : Straight through the center of the lens into the other side.

Concave or Diverging Lens FF do=f

Concave or Diverging Lens FF do=f Ray 1

Concave or Diverging Lens FF do=f Ray 1 Ray 2

Concave or Diverging Lens FF do=f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF do=f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF do=f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF do=f Ray 1 Ray 2 Ray 3 Image Virtual Right Side Up Demagnified

Concave or Diverging Lens FF do>2f

Concave or Diverging Lens FF do>2f Ray 1

Concave or Diverging Lens FF do>2f Ray 1 Ray 2

Concave or Diverging Lens FF do>2f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF do>2f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF do>2f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF do>2f Ray 1 Ray 2 Ray 3 Image Virtual Right Side Up Demagnified

Concave or Diverging Lens FF f<do<2f

Concave or Diverging Lens FF f<do<2f Ray 1

Concave or Diverging Lens FF f<do<2f Ray 1 Ray 2

Concave or Diverging Lens FF f<do<2f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF f<do<2f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF f<do<2f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF f<do<2f Ray 1 Ray 2 Ray 3 Image Virtual Right Side Up Demagnified

Concave or Diverging Lens FF do<f

Concave or Diverging Lens FF do<f Ray 1

Concave or Diverging Lens FF do<f Ray 1 Ray 2

Concave or Diverging Lens FF do<f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF do<f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF do<f Ray 1 Ray 2 Ray 3

Concave or Diverging Lens FF do<f Ray 1 Ray 2 Ray 3 Image Virtual Right side Up Demagnified

Sign Conventions (Spherical Mirrors & Lenses) QuantityConditionsSign Focal Length f Concave Mirror + Remember one remember all Convex Mirror - CCM is Positive Convex Lens + Concave Lens - Object Distance (do) Mostly Always + Image Distance (di) Image Real + Does not depend on side it is on. Image Virtual - Magnification (M) Image Upright + Image Inverted -

Spherical MirrorsSpherical Lenses ConcaveConvex (Converging) Concave (Diverging) ConditionResultsConditionResultsConditionResultsConditionResults do=fNo Imagedo>R Virtual Right side up Demagnified do=fNo imagedo=f Virtual Right Side Up Demagnified f<do<R Real Upside down. Magnified. f<do<R Virtual Right side up Demagnified f<do<2f Real Upside Down Magnified do>2f Virtual Right Side Up Demagnified do>R Real Demagnified Upside Down do<f Virtual Right side up Demagnified do>2f Real Upside Down Demagnified f<do<2f Virtual Right Side Up Demagnified do<f Virtual Magnified Right Side up do<f Virtual Right Side up Magnified do<f Virtual Right Side Up Demagnfied do=R Real Upside Down Demagnified do=2f Real Upside Down Magnified

Concave MirrorConvex Mirror 1.First ray goes parallel to the mirror and then reflects back down through the focus. 2.Second Ray goes through the focus and into the mirror and then reflected back parallel to axis. 3.Ray drawn to center of lens and reflects back downwards at an equal angle (symmetric) 4.If at or within the focal length you an draw a line perpendicular to the mirror so that it goes back through itself and into the center of curvature (R = 2f). This can replace the second ray above which now cannot be drawn. 1.First ray goes parallel to the mirror and then reflects back up (dotted image line goes through focus on the other side). 2.Second Ray is aimed directly at the center of curvature on the other side but once it hits the mirror it reflects back through itself with the dotted image line going through C). 3.Ray drawn aimed at focus on the other side and reflect off the mirror parallel to the axis (dotted line drawn parallel in the other direction) Concave LensConvex Lens 1.1 st ray is drawn parallel to principle axis and hits the lens. It will refract upwards with its reversibility going through the focal point on the same side. 2.2 nd ray is drawn from the object in a direction diagonal to the focal point on the other side but goes parallel to the principal axis once it crossed the lens. 3.3 rd ray is drawn from the object straight through the center of the lens. 1.First ray is drawn parallel to principal axis until it strikes the center of the mirror. It then converged down on through the focal point on the other side of the lens. 2.The second ray has a straight line drawn from the object to the focus to the lens on the same side and then it refracts parallel to the principal axis on the other side. 3.The third ray is usually drawn in a direction from the object through the center of the lens itself into the other side.