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
Your initial equation is correct: 1/f = 1/d(object) + 1/d(image). However, your calculations afterward are incorrect. Here's how to properly approach the problem:
Given:
focal length (f) = 0.035m
distance to the object (d(object)) = 6m
We need to find the distance to the image (d(image)).
Substituting the given values into the equation:
1/0.035 = 1/6 + 1/d(image)
To simplify the equation, we can find a common denominator:
1/d(image) = 1/0.035 - 1/6
Let's calculate this:
1/d(image) = (6 - 0.035) / (0.035 * 6)
= (5.965) / (0.21)
Now, we can find the reciprocal of both sides of the equation:
d(image) = (0.21) / (5.965)
≈ 0.035258 m
So, the film needs to be approximately 0.035258 meters away from the lens to record a clear image.
Your approach is correct, but there seems to be a calculation error. Let's go through the steps again to find the correct distance.
We can use the lens formula: 1/f = 1/d(object) + 1/d(image)
Given:
Focal length (f) = 0.035m
Distance from object to lens (d(object)) = 6m
Distance from film to lens (d(image)) = unknown
Plugging the values into the equation, we get:
1/0.035 = 1/6 + 1/d(image)
To simplify the equation, we first need to find the common denominator for 1/6 and 1/d(image). The common denominator is 6 * d(image).
Now we can rewrite the equation as:
1/0.035 = (1 * 6 * d(image))/(6 * d(image)) + (1 * 0.035)/(6 * d(image))
Simplifying further:
1/0.035 = (6 * d(image) + 0.035)/(6 * d(image))
Cross-multiplying the equation gives:
(6 * d(image))(1) = (0.035)(6 * d(image) + 0.035)
Simplifying this equation:
6 * d(image) = 0.035 * (6 * d(image) + 0.035)
Expanding the expression:
6 * d(image) = 0.21 * d(image) + 0.0001225
Isolating the variable d(image) gives:
6 * d(image) - 0.21 * d(image) = 0.0001225
Combining like terms:
5.79 * d(image) = 0.0001225
Divide both sides by 5.79 to solve for d(image):
d(image) = 0.0001225 / 5.79
Calculating this gives:
d(image) ≈ 2.115e-5 m
Therefore, the film needs to be approximately 2.115e-5 meters (or 0.02115 mm) away from the lens in order to record a clear image.