Camera lenses are described in terms of their focal length. A 50.0 mm lens has a focal length of 50.0 mm
(a) A camera with a 50 mm lens is focused on an object 4.0 m away. Locate the image.
(b) A 980 mm lens is focused on an object 125 m away. Locate the image.
okat so yu do wavberlnth abnd then dividwe by 100
(a) Well, if we have a camera with a 50 mm lens and it's focused on an object 4.0 m away, the image will probably be somewhere in the camera, don't you think? But seriously, let's do the math. We can use the lens equation:
1/f = 1/di - 1/do
where f is the focal length, di is the image distance, and do is the object distance. Plugging in the values, we get:
1/50 = 1/di - 1/4000
Let's solve for di:
1/di = 1/50 + 1/4000
1/di = (4000 + 50)/50*4000
1/di = 4050/200000
di = 200000/4050
di = 49.38 mm
So the image is located approximately 49.38 mm away from the camera.
(b) Now for the 980 mm lens focused on an object 125 m away. Let's apply the lens equation once again:
1/f = 1/di - 1/do
Plugging in the values:
1/980 = 1/di - 1/125
Solving for di:
1/di = 1/980 + 1/125
1/di = (125 + 980)/125*980
1/di = 1105/1225000
di = 1225000/1105
di ≈ 1108.60 mm
So the image is located approximately 1108.60 mm away from the camera.
To locate the image in both scenarios, we can use the lens formula:
1/f = 1/d₀ + 1/dᵢ
where:
- f is the focal length of the lens
- d₀ is the distance between the lens and the object
- dᵢ is the distance between the lens and the image
Let's solve the problems step-by-step:
(a) A 50 mm lens with a focal length of 50 mm is focused on an object 4.0 m away.
Given:
focal length (f) = 50 mm = 0.050 m
distance from the lens to the object (d₀) = 4.0 m
To find:
The distance from the lens to the image (dᵢ).
Using the lens formula:
1/f = 1/d₀ + 1/dᵢ
Substituting the given values:
1/0.050 = 1/4.0 + 1/dᵢ
Now, let's solve for dᵢ:
1/dᵢ = 1/0.050 - 1/4.0
Calculating this gives us:
1/dᵢ = 20 - 0.25 = 19.75
Taking the reciprocal of both sides:
dᵢ = 1/19.75 ≈ 0.051 m
Therefore, the image is located approximately 0.051 meters away from the lens.
(b) A 980 mm lens with a focal length of 980 mm is focused on an object 125 m away.
Given:
focal length (f) = 980 mm = 0.980 m
distance from the lens to the object (d₀) = 125 m
To find:
The distance from the lens to the image (dᵢ).
Using the lens formula:
1/f = 1/d₀ + 1/dᵢ
Substituting the given values:
1/0.980 = 1/125 + 1/dᵢ
Now, let's solve for dᵢ:
1/dᵢ = 1/0.980 - 1/125
Calculating this gives us:
1/dᵢ = 1.020 - 0.008 = 1.012
Taking the reciprocal of both sides:
dᵢ = 1/1.012 ≈ 0.988 m
Therefore, the image is located approximately 0.988 meters away from the lens.
To locate the image in each scenario, we can use the lens formula:
1/f = 1/d₁ + 1/d₂
Where:
- f is the focal length of the lens
- d₁ is the object distance (distance of the object from the lens)
- d₂ is the image distance (distance of the image from the lens)
Let's solve each part of the question step by step:
(a) A camera with a 50 mm lens is focused on an object 4.0 m away.
First, we need to convert the object distance to meters, as the focal length of the lens is given in millimeters:
Object distance, d₁ = 4.0 m = 4000 mm
Now, we can substitute the given values into the lens formula:
1/50 mm = 1/4000 mm + 1/d₂
To solve for d₂, we rearrange the equation:
1/d₂ = 1/50 mm - 1/4000 mm
Now, we can calculate the value of 1/d₂:
1/d₂ = 0.02 - 0.00025
1/d₂ = 0.01975
Taking the reciprocal of both sides, we find:
d₂ ≈ 50.63 mm
Therefore, the image in this scenario is located approximately 50.63 mm away from the lens.
(b) A 980 mm lens is focused on an object 125 m away.
We need to convert the object distance to millimeters:
Object distance, d₁ = 125 m = 125000 mm
Substituting the values into the lens formula:
1/980 mm = 1/125000 mm + 1/d₂
To solve for d₂:
1/d₂ = 1/980 mm - 1/125000 mm
Calculating the value of 1/d₂:
1/d₂ = 0.00102 - 8.0 x 10^(-6)
1/d₂ ≈ 0.00101
Taking the reciprocal:
d₂ ≈ 990.1 mm
So, the image in the second scenario is located approximately 990.1 mm away from the lens.
1/do+1/di=1/f
1/4+1/di=1/.05
.25+1/di=20
di=1/19.75= you do it.