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.
To determine the distance from the 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 (200mm),
- v is the image distance (distance between the lens and the film, 201mm), and
- u is the object distance (distance between the lens and the bird).
Let's substitute the given values into the formula:
1/200 = 1/201 - 1/u
Now, let's solve for u:
1/u = 1/200 - 1/201
Combining the fractions:
1/u = (201 - 200) / (200 * 201)
= 1 / (200 * 201)
Inverting both sides of the equation:
u = (200 * 201) / 1
= 40,200 mm
Therefore, the distance from the lens to the bird is 40,200 mm.
To find the distance from the 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 (given as 200mm)
- v is the image distance (distance from the lens to the film, given as 201mm)
- u is the object distance (distance from the lens to the bird, which we need to find)
Rearranging the formula, we get:
1/u = 1/f - 1/v
Substituting the given values:
1/u = 1/200 - 1/201
To simplify the calculation, let's find a common denominator for 200 and 201:
1/u = (201 - 200) / (200 * 201)
1/u = 1 / (200 * 201)
Now, we can take the reciprocal of both sides to isolate u:
u = (200 * 201) / 1
Simplifying:
u = 40,200 mm
Therefore, the distance from the lens to the bird is 40,200 mm.