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University of Wisconsin - Milwaukee

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Problem 3 Medium Difficulty

An $f / 2.80$ CCD camera has a $105-\mathrm{mm}$ focal length lens and can focus on objects from infinity to as near as 30.0 $\mathrm{cm}$ from the lens. (a) Determine the camera's aperture diameter. Determine the (b) minimum and (c) maximum distances from the CCD sensor over which the lens must be able to travel during focusing. Note: "f/2.80" means "an $f$ -number of 2.80 ."

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Video Transcript

So in this problem we have a CCD camera which has a focal length of 105 millimeter and F number. He calls 2.8. So we also know that the camera can focus an object from infinity down to 30 centimeter. So what that means is the object distance can be P wa Nichols Infinity down to p two equals 300 millimeter. So to solve the problem, eh? Which is to find the diameter of the pressure of the lens. All we need to do is just use the definition off F number. So let's do that. So the definition of the F number is the ratio between the focal length of the less and the diameter of the pressure. Right. So from here, the diameter of the printer D is F over F number, which is 100 or five millimeter over 2.8. This is going to give us 37.5 millimeter. So this is, uh, diameter of the oppressor. All right, so let's go to part B in part B. We want to find out the minimum distance between the lens and the CCD sensor. Remember, that is also the emits a sense, so that's what matters. So to find the minimum distance, we have to assume that the object is at infinity. All right, So for part B, we are actually going to use object distance at infinity, which is P one equals infinity. Now, if we use the less equation, which is what over F? Because one of her p one plus whatever kyu won from here, we know one over p one equals one of her infinity, which is zero. So that means act is going to be called a key one, right? So we're actually trying to find the Q one, so Q one is going to be cool to act, which is 105 millimeter. All right, so pretty straightforward, right? So let's do party, which is the maximum distance between the lens and the CCD sensor. Now, in this case, we're actually going to assume P one because 300 millimeter, which is the close range of the camera closest where the camera can focus. So we will do the same thing again, used, uh, less equation, and in this case, I'm gonna write it down straight, so Q one, because P the p one dot Sorry. This is this is P two and cute too. So I'm gonna write that down first. Yes. So P two and cute too. All right, p two times. Cute F over P two minus f. So this is going to be 300 times. 105 300 times. 105 over 300 minus 105. And this will give me 161.5 millimeter. So this is the the longest distance between the the CCD and a lens. So that means the shortest distance between the range is 105 from 105 261 0.5 millimeter.

University of Wisconsin - Milwaukee
Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Zachary M.

Hope College