Setting up an optical sensor with a dot sequence

[confuzzled1]

Homework Statement

Needan optical sensor to detect a dot sequence on widgets passing 50cm away from the sensor. Want each dot to exactly cover the sensor. If the dots are 10mm in diameter and the sensor is 40mm in diameter, what is the position and focal length of the lens to do the focusing.

Homework Equations

m=-di/do
1/do+1/di=1/f

The Attempt at a Solution

m=-di/50cm
1/50cm+1/di=1/f
not sure what number is di, f, or m; if I knew one of these I could finish the problem.

 

[OlderDan]

It looks to me like you need for do + di to be 50cm, so you do not have the right number for do. My initial reaction is that their could be a range of focal lengths with the lens in the proper position that could work, so you might not be looking for a unique solution. Allow for that possibility if you can't find enough equations to solve for the number of variables you have. If that turns out to be the case, you will probably want to choose the lens that keeps the neigboring dot images as far apart as possible.

 

[confuzzled1]

Thank you very much. We only covered this in a coule of days(Microprocessors) and I don't have this in physics until next semester. I'll try again and repost!

 

[confuzzled1]

Reworked

di + do = 50cm or 500 mm
M= 40mm
So, 40mm= di/do
40di = do
do + 40 do= 500mm
41do= 500mm
500mm /41 do = do
do = 12.2mm 500-12.2=di di= 487.8

1/f= 1/487.8 + 1/12.2 1/f= 499/5844 5844/499= f
f= 11.7mm

I just might have it could you recheck for me, please?

 

[OlderDan]

di + do = 50cm or 500 mm
M= 40mm
So, 40mm= di/do
40di = do
do + 40 do= 500mm
41do= 500mm
500mm /41 do = do
do = 12.2mm 500-12.2=di di= 487.8

1/f= 1/487.8 + 1/12.2 1/f= 499/5844 5844/499= f
f= 11.7mm

I just might have it could you recheck for me, please?

The magnification is not 40mm. Magnification is a ratio of lengths and is dimensionless. You want the image to be 4 times the size of the object, so you will need m = -di/do = -4. The - is because it will be a real inverted image. So you have di = 4do. This does lead to a unique solution for f and position for the lens. Try it one more time.

 

[confuzzled1]

i got F= 80! I handed it in today get it back Friday. Thank you so very much for helping me with this!

 

[OlderDan]

i got F= 80! I handed it in today get it back Friday. Thank you so very much for helping me with this!

I hope that 80 is in mm