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Classical Mechanics Level 2

Recently there have been technological advances that allow for 3-d imaging up to kilometers away of an object. This can be done by using laser light that bounces off an object. By measuring the time it takes the laser light to get to the object and back, one can construct a detailed 3-d image of the object. The obstruction has been to get enough of the light back to actually make an image, but new detectors are sensitive enough to overcome this limitation.

If I want to measure a 3-d object down to millimeter accuracy, to what accuracy in seconds must my detector be able to measure the time of arrival of the light that bounced off the object?

Remember... the light has to bounce there and back.

Details and assumptions

The speed of light is $3 \times 10^8~\mbox{m/s}$ .

The answer is 6.67E-12.

1 solution

Thomas Jones
Sep 23, 2013

In this question, you have to find out how long the light would take to travel from its source to the object and back again when the object is only 1mm away. The speed of light is constant so you are able to use:

$Speed = \frac{Distance}{Time}$

Rearranged for Time:

$Time = \frac{Distance}{Speed}$

As time is in $ms^{-1}$ you have to convert the total distance covered by the light into meters:

$Distance = 0.002m$

Put this into the equation for time:

$Time = \frac{0.002}{300000000}$

Therefore the accuracy for Time is:

$6.67$ x $10^{-12}$

how we can distance

Sai Chaturvedula - 7 years, 8 months ago

If you want to measure down to millimeter accuracy then the accuracy of your timer has to be the same as the time taken for light to return from the object if it was $1mm$ away, so a total distance of $2mm$ or $0.002m$ has to be used to determine this.

Thomas Jones - 7 years, 8 months ago

i answered 0.6e-11..is it incorrect?

Utkarsh Verma - 7 years, 8 months ago

You need to give your answer to 3 significant figures and it is always best to have it in the form 6.67e-12 rather than 0.667e-11 even though they are the same thing.

Thomas Jones - 7 years, 8 months ago

The significand must be between $1\leq a<10$ for scientific notation $a\cdot 10^{b}$ . This is sometimes confused with the binary mantissa, written in binary in the form $1.\bar{m} \times 2^{n}$ commonly used in IEEE, electrical engineering, and numerical analysis in programming.

Jerry McKenzie - 3 years, 5 months ago

I forgot to consider that the light was reflected...... So got it wrong.

Siddhant Chaudhari - 5 years, 5 months ago

For a more general solution, you can show that this is the time difference the light takes when it goes to a distance $x$ versus when it goes to a distance $x+10^{-3}$ .

Harsh Poonia - 2 years, 3 months ago

I see you, you can't hide from me!

The answer is 6.67E-12.

1 solution

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