How do you draw a lenses ray diagram ?

Question

An object 1.5 cm high is located 7.00 cm in front of a converging lens that has a focal length of 5.00 cm. Draw the ray diagram to scale. Find the image distance, image height and the magnification of the image. Confirm your results with the lens equation and the magnification equation. Show your math.

Answer 1

Hi Ayo! 

 

To set this up, first choose a scale (you can do 1 cm on the page for every 1 cm in the problem, for example; a "one-to-one" scale). 

 

Then draw your converging lens.  This lens will be wider in the middle than at the ends.  Also draw, perpendicular to the lens and all the way across your paper, a dashed line.  This will be the "axis," and the distance from the lens to its focal points and any objects or images are measured along this line.

 

Five centimeters (on your scale) to either side of the lens, put a dot on the axis.  These are the two "focal points" of the lens.

 

Go 7 cm to the left of the lens.  Draw an arrow, pointing up and perpendicular to the axis, which is 7 cm (on your scale) high.  This is the object.

 

Now, there are two "principal rays" which can be used to locate the image of a converging lens.  Draw the two rays as arrows originating from the tip of the object arrow, heading toward the lens.

 

The FIRST ray will be parallel to the axis as it goes from the object to the lens.  The rule for this ray is that, once it goes through the lens, it gets redirected through the focal point on the opposite side from the object.

 

The SECOND ray will go from the top of the object arrow toward the middle of the lens, where the axis intersects it.  The rule for this ray is that it goes straight through the lens, without being deviated.

 

Look for a point where the rays cross once they come out of the lens.  If they cross, draw an arrow perpendicular to the axis which points toward the crossing point of the two rays.  The ends of that arrow should be on the axis and the crossing point.  This will be a REAL image (since the rays actually cross in space).

 

If the rays coming out of the lens do not appear as if they are going to intersect, start at the lens and extend each emerging ray BACKWARDS (as straight dashed lines) to the object side of the lens.  This represents the line that it LOOKS like the emerging rays came from.  They will cross at a point, and you draw the same arrow a above from the axis perpendicular to that point.  This will be a VIRTUAL image, since the rays do not actually cross at that point, but only APPEAR to if you look back along the emerging rays through the lens.

 

[I suspect that with the given conditions, you should get a real image]

 

If you make your drawing carefully, with rulers (and perhaps graph paper), you should be able to measure accurately the position and size of your image, and have those numbers match what you would get out of the lens equation.

 

I hope this helps!  I know if it can be difficult to picture without diagrams or the ability to ak immediate questions, but if you have any other questions or concerns, or would like to check an answer, please let me know.