ACTICS BOX $18\mathrm{.}2$ Ray tracing for a converging lens

Draw an optical axis. Use graph paper or a ruler Establish an appropriate scale

Center the lens on the axis. Draw the lens plane perpendicular to the axis through the center of the lens. Mark and label the focal points at distance $f$ on either side.

Represent the object with an upright arrow at distance $s.$ It is usually best to place the base of the arrow on the axis and to draw the arrow about half the radius of the lens.

Draw the three "special rays" from the tip of the arrow. Use a straightedge or a ruler. The rays refract at the lens plane, not at the surfaces of the lens.

a$.$ A ray initially parallel to the axis $($Ray $1)$ refracts through the far focal point.

b$.$ A ray that enters the lens along a line through the near focal point $($Ray $2)$ emerges parallel to the axis.

c$.$ A ray through the center of the lens $($Ray $3)$ does not bend

Extend the rays until they converge. The rays converge at the image point. Draw the rest of the image in the image plane. If the base of the object is on the axis, then the base of the image will also be on the axis.

Measure the image distance $s^{\text{'}}.$ Also, if needed, measure the image height relative to the object height. The magnification can be found from $m=-\frac{s^{\text{'}}}{s}.$

Follow the steps above to solve the following problem: An object is $9\mathrm{.}0$ cm from a converging lens with a focal length of $2\mathrm{.}8$ cm $.$ Use ray tracing to determine the location of the image.

Part A

The diagram below shows the situation described in the problem. The focal length of the lens is labeled $f$; the scale on the optical axis is in centimeters. Draw the three special rays, Ray$1,$ Ray$2,$ and Ray$3$ as described in the Tactics Box above, and label each ray accordingly. Draw the rays from the tip of the object to the center vertical axis of the lens. Do not draw the refracted rays.

Draw the vectors for the incident rays starting at the tip of the object to the center vertical axis of the lens. The location and orientation of the vectors will be graded.

I

Ray $3$ Ray though center of lens

Ray $2$ Ray through near focal point

Ray $1$ Ray parallel to axis

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