a camera with a 200mm lens(focal length) makes a real image of a bird on film.The film is located 201 mm behind the lens.Determine the distance from the lens to the bird.
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Use the lens equation:
1/0bject distance + 1/imagedistance= 1/focal length.
To determine the distance from the lens to the bird, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = distance of the image from the lens (in this case, it is the distance between the lens and the film)
u = distance of the object from the lens (in this case, it is the distance between the lens and the bird)
Let's substitute the given values into the formula:
1/200 = 1/201 - 1/u
Next, let's simplify the equation by finding a common denominator:
1/200 = (201 - u)/201u
Now, let's cross multiply:
u = (1/200) * 201u - (1/200) * 201
Simplifying further:
u = u/200 - 201/200
Combining like terms:
u - u/200 = -201/200
Multiplying through by 200:
200u - u = -201
Simplifying:
199u = -201
Finally, we can solve for u by dividing both sides by 199:
u = -201/199
Therefore, the distance from the lens to the bird is approximately -1.0101 mm.
To determine the distance from the camera lens to the bird, we can use the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- v is the image distance (distance between the lens and the film)
- u is the object distance (distance between the lens and the bird)
We are given:
- f = 200 mm
- v = 201 mm (since the film is located 201 mm behind the lens)
- u (to be determined)
Substituting the given values into the lens formula:
1/200 = 1/201 - 1/u
To solve for u, we can rearrange the equation:
1/u = 1/200 - 1/201
Taking the reciprocal of both sides, we get:
u = 1 / (1/200 - 1/201)
Now, let's simplify the equation:
u = 1 / ((201 - 200) / (200 * 201))
u = 1 / (1 / (200 * 201))
u = 200 * 201
Therefore, the distance from the lens to the bird is 40,200 mm (or 40.2 meters).