Setting up an optical sensor with a dot sequence

In summary, the homework statement is trying to find a lens that will detect a dot sequence on widgets passing 50cm away from the sensor. It wants each dot to exactly cover the sensor. If the dots are 10mm in diameter and the sensor is 40mm in diameter, the lens should be positioned and focal length to do the focusing.
  • #1
confuzzled1
4
0

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.
 
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  • #2
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.
 
  • #3
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!
 
  • #4
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?
 
  • #5
confuzzled1 said:
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.
 
  • #6
i got F= 80! I handed it in today get it back Friday. Thank you so very much for helping me with this!
 
  • #7
confuzzled1 said:
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 :smile:
 

1. How does an optical sensor with a dot sequence work?

An optical sensor with a dot sequence works by emitting a beam of light and measuring the reflection or absorption of this light by the surface it is pointed at. The dot sequence refers to the specific pattern of dots that the sensor emits, which helps to accurately detect changes in surface texture or distance.

2. What types of materials can an optical sensor with a dot sequence be used on?

An optical sensor with a dot sequence can be used on a wide range of materials, including metal, plastic, wood, fabric, and even liquids. As long as the material has some level of reflectivity or absorption, the sensor should be able to detect it.

3. How accurate is an optical sensor with a dot sequence?

The accuracy of an optical sensor with a dot sequence depends on several factors, including the quality of the sensor itself, the surface being measured, and the distance between the sensor and the surface. Generally, these sensors have a high level of accuracy, with some models being able to detect changes as small as 0.01mm.

4. Can an optical sensor with a dot sequence be used in different lighting conditions?

Yes, most optical sensors with a dot sequence are designed to work in various lighting conditions, including both natural and artificial light. However, extreme lighting conditions, such as direct sunlight or complete darkness, may affect the sensor's accuracy and performance.

5. How can I calibrate an optical sensor with a dot sequence?

The process of calibrating an optical sensor with a dot sequence will vary depending on the specific model and manufacturer. However, most sensors will come with a calibration tool or software that allows you to adjust the sensor's settings for optimal performance. It is essential to follow the manufacturer's instructions carefully to ensure accurate and reliable measurements.

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