Ray+Trace+Diagrams

= Ray Trace Diagrams =

In physics, a **ray trace** diagram is used to track the trajectory of a beam of light as it passes through or reflects either a mirror or a lens. The beam is drawn as it passes through the **focus** point (f), twice the focus point (2f), and parallel to the **principal axis**. In general, separate diagrams are made for the beams at distances of >2f, 2f, 2f>f, f, and >f, as each has it's own characteristics. The diagram is different for mirrors and lenses and also fluctuates depending on **concavity**. Ray trace diagrams are the science behind almost everything involving **optics**, including telescopes, binoculars, microscopes, and even cameras. The diagram will also predict if the projected image will be real or virtual, as well as the orientation and size of the image.

Finding the Focus
To find the focus point use the equation 1/p + 1/q = 1/f, this is known as the **Thin Lens Equation**. Where p is the distance from the object, q is half the radius of the mirror, and f is the distance from the mirror to the focus. If the object projecting the beam is very far away, such as the sun, then 1/p = 0. Therefore, in such cases the focus is located at r/2. By simple arithmetic you can conclude that a mirror with r = 1 inch has a focus located 2 inches from it. r/2 = 1/f 1/2 = 1/f f=2 To find the size of the image the equation used is M= -di/do or in words **negative** image distance divided by object distance. A non-mathematical way to solve a problem like this would be to angle your mirror towards the sun, focusing the reflected light on a sheet of paper. When the point of light is sharpest measure the distance from the paper to the mirror. This is the focal length.

**For Mirrors**

 * 1) Ray 1 is drawn **parallel** to the principal axis and is reflected back through the focal point.
 * 2) Ray 2 is drawn through the focal point and is reflected parallel to the principal axis.
 * 3) Ray 3 is drawn through 2f, and is reflected back on itself.



Ray 1 is drawn parallel to the **principal** axis. After being refracted by the lens, this ray passes through or appears to come from one of the focal points.
 * For Lenses**
 * 1) Ray 2 is drawn through the **center** of the lens. This ray continues in a straight line.
 * 2) Ray 3 is drawn through the other **focal** point and emerges from the lens parallel to the principal axis.



Charts
To simplify, all the information that can be gathered is traditionally put into a chart. The chart for convex mirrors being the same as concave lenses, and the chart for concave mirrors the same as the chart for convex lenses.

Concave mirror

 * Do ||  Di  ||  orientation  ||  nature  ||  size  ||
 * >2f ||  2f> >f  ||  down  ||  R  ||  small  ||
 * 2f ||  2f  ||  down  ||  R  ||  same  ||
 * 2f> >f ||  >2f  ||  down  ||  R  ||  big  ||
 * f ||  inf.  ||  down  ||  V  ||  big  ||
 * >f ||  negative  ||  up  ||  V  ||  big  ||

**Convex mirror**

 * Do ||  Di  ||  orientation  ||  nature  ||  size  ||
 * >2f ||  2f> >f  ||  down  ||  R  ||  small  ||
 * 2f ||  2f  ||  down  ||  R  ||  same  ||
 * 2f> >f ||  >2f  ||  down  ||  R  ||  big  ||
 * f ||  inf.  ||  x  ||  x  ||  x  ||
 * >f ||  Same side  ||  up  ||  V  ||  big  ||

**Concave lens**

 * Do ||  Di  ||  orientation  ||  nature  ||  size  ||
 * >2f ||  2f> >f  ||  down  ||  R  ||  small  ||
 * 2f ||  2f  ||  down  ||  R  ||  same  ||
 * 2f> >f ||  >2f  ||  down  ||  R  ||  big  ||
 * f ||  inf.  ||  x  ||  x  ||  x  ||
 * >f ||  Same side  ||  up  ||  V  ||  big  ||


 * Do ||  Di  ||  orientation  ||  nature  ||  size  ||
 * >2f ||  2f> >f  ||  down  ||  R  ||  small  ||
 * 2f ||  2f  ||  down  ||  R  ||  same  ||
 * 2f> >f ||  >2f  ||  down  ||  R  ||  big  ||
 * f ||  inf.  ||  down  ||  V  ||  big  ||
 * >f ||  negative  ||  up  ||  V  ||  big  ||

**Examples *1/o + 1/i = 1/f is the same as 1/p + 1/q =1/f* (**1/o = object distance and 1/i = image distance)
See bottom for answers to the examples !!!! 1) The object is 12 cm, the focal length is - 5 and the center is - 12, find the image distance. 1/i + 1/o= 1/f (equation) (a negative answer means the image is on the opposite side of the mirror than the object, which makes the image virtual)
 * Step One :** 1/i + 1/ 12= 1/-5 (plug what you know into the equation)
 * Step Two:** 1/i = 1/-5 - 1/12 ( subtract 1/o to get 1/i by itself, so you can solve for it)
 * Step Three:** 1/i= 12/-60 - 5/60 ( find common denominators)
 * Step Four**: 1/i = -17/60 (subtract the object distance from the focal length)
 * Step Five:** i= 60/-17 = ... ( flip the fraction over to get i instead of 1/i and divide to find the image distance)

2) The object = 14 cm Focal Length =4 cm Center =7 cm. To find the image you use the equation 1/0+1/i =1/f . 3) The object is 5cm, the focal length is 9 cm, and the center is 16 cm. 1/o+ 1/i =1/f 4) The object is 10 cm, the focal length is -6 cm, find the image distance. 1/o +1/i = 1/f
 * Step One**: 1/14+1/i= 1/4
 * Step Two**: 1/i =1/4 - 1/14
 * Step Three** : 1/i = 7/28 - 2/28
 * Step Four**: 1/i = 5/28
 * Step Five:** i=28/5 =.....
 * Step One:** 1/5 + 1/i = 1/9
 * Step Two:** 1/i = 1/9 - 1/5
 * Step Three**: 1/i = 5/45 - 9/45
 * Step Four** : 1/i= -4/45
 * Step Five:** i= 45/-4 = .....
 * Step One**: 1/10 + 1/i = 1/-6
 * Step Two**: 1/i = 1/-6 - 1/10
 * Step Three:** 1/i = 5/-30 - 3/30
 * Step Four:** 1/i = -8/30
 * Step Five:** i = 30/-8 = ....
 * Because the image distance is negative the image size (M= -di/do) will be positive so the image is **upright,** **virtual,** and **smaller** than the object**.**

5) The object is 10 cm, the focal length is 4 cm, and the center is 8 cm, find the image distance.
 * 1/i + 1/o = 1/f**
 * S****tep One:** 1/i + 1/ 10 =1/4
 * Step Two:** 1/i = 1/4-1/10
 * Step Three:** 1/i=10/40-4/10
 * Step Four:** 1/i = 6/40
 * Step Five:** i = 40/6 =......

Answers : **1)** -3.53 cm **2**) 5.6 cm **3)** -11.25 **4**) -3.75 cm **5)** -3.75 cm

**Works Cited** Diagram for problem 5 “Core Unit III: Light.” //Physics 20-Light Reflection//. N.p., n.d. Web. 1 June 2012. .// // Diagrams for problems 2,3,4 “Ray Diagrams for Mirrors .”// Hyperphysics //. N.p., n.d. Web. 1 June 2012. .// // Diagrams for problem 1 Stoner, Ellen.// Mirror Ray Tracing//. N.p., 25 Dec. 2005. Web. 1 June 2012. .
 * Reference**

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