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
FC
• do = f
Ray 1Cannot Draw 2nd ray from Object through focus.
Ray 3
They do not Cross:
No Image!
Concave Mirror
FC
• do = f
Ray 1Cannot 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
The Rays appear to be pretty much parallel.
Therefore they will not cross on either side so
there is no image, virtual or real.
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<do>R
• do<f
Convex or Converging Lens
• For the Following Conditions
do=f f<do<2f do>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 3The 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
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!
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<do<2f do>2f do<f
• Note the lens thickness is to be assumed small so that refraction is not a concern.
Rules for Concave Lenses
• 1st 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.
• 2nd 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.
• 3rd 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 3Rule Three : Straight
through the center of the lens into the other side.
Sign Conventions (Spherical Mirrors & Lenses)
Quantity Conditions Sign
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 Mirrors Spherical Lenses
Concave ConvexConvex
(Converging)Concave
(Diverging)
Condition Results Condition Results Condition Results Condition Results
do=f No Image do>R
Virtual
Right side up
Demagnified
do=f No image do=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 Mirror Convex 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 Lens Convex Lens
1. 1st 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. 2nd 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. 3rd 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.