If I had the old-fashion camera that had a focal length of 35mm(0.035m) and I take a picture of a person 6 m away, how far does the film need to be from the lens to record a clear image?

I know that the equation is 1/f = 1/d(object) + 1/d(image) so would I do the following:
1/0.035m = 1/6 +1/unknown
28.57 = .1666+ 1/unknown
28.57-.1666=28.40
di=1/28.40 = .035m
Is this even close or all wrong-it doesn't sound correct

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Your approach is mostly correct, but there is a small error in your calculations. Let's go through the correct steps to find the distance of the film from the lens.

The lens equation you mentioned, 1/f = 1/d(object) + 1/d(image), is the right equation to use. Here's how you can apply it:

Given:
- Focal length, f = 0.035m
- Distance to the object, d(object) = 6m
- Distance to the image, d(image) = unknown

Step 1: Substitute the values into the lens equation
1/f = 1/d(object) + 1/d(image)

Substituting the known values:
1/0.035 = 1/6 + 1/d(image)

Step 2: Simplify the equation
To simplify the equation, you need to find a common denominator for the two fractions on the right-hand side. In this case, the common denominator is 6d(image) since it's the product of the denominators.

Multiplying both sides of the equation by 6d(image), we get:
6d(image)/0.035 = 6d(image)/6 + 6/(d(image))

Simplifying further:
171.43d(image) = d(image) + 6

Step 3: Solve for d(image)
To isolate d(image), we need to move the terms with d(image) to one side of the equation and the constant terms to the other side.

171.43d(image) - d(image) = 6

Simplifying further:
170.43d(image) = 6

Step 4: Solve for d(image)
Now, divide both sides of the equation by 170.43 to solve for d(image):
d(image) = 6 / 170.43

Calculating this value gives you:
d(image) ≈ 0.035228m

So, the distance of the film from the lens should be approximately 0.035228m to record a clear image of a person 6m away.