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.

To answer these questions, we will be using the thin lens formula, which relates the object distance (denoted as "d₀"), the image distance (denoted as "dᵢ"), and the focal length (denoted as "f") of the lens:

1/f = 1/d₀ + 1/dᵢ

(a) For the first question, where the camera has a 50 mm lens and is focused on an object 4.0 m away:

Step 1: Convert the focal length from millimeters to meters:
f = 50 mm = 50 × 10⁻³ m = 0.050 m

Step 2: Identify the given values:
f = 0.050 m
d₀ = 4.0 m (object distance)
dᵢ = ? (image distance)

Step 3: Apply the thin lens formula:
1/f = 1/d₀ + 1/dᵢ

Substituting the known values:
1/0.050 = 1/4.0 + 1/dᵢ

Simplifying the equation:

1/0.050 - 1/4.0 = 1/dᵢ

Step 4: Calculate the image distance:
dᵢ = 1 / (1/0.050 - 1/4.0)

Using a calculator, we find:
dᵢ ≈ 0.0518 m

Therefore, the image is located approximately 0.0518 meters away from the lens.

(b) For the second question, where a 980 mm lens is focused on an object 125 m away:

Step 1: Convert the focal length from millimeters to meters:
f = 980 mm = 980 × 10⁻³ m = 0.980 m

Step 2: Identify the given values:
f = 0.980 m
d₀ = 125 m (object distance)
dᵢ = ? (image distance)

Step 3: Apply the thin lens formula:
1/f = 1/d₀ + 1/dᵢ

Substituting the known values:
1/0.980 = 1/125 + 1/dᵢ

Simplifying the equation:

1/0.980 - 1/125 = 1/dᵢ

Step 4: Calculate the image distance:
dᵢ = 1 / (1/0.980 - 1/125)

Using a calculator, we find:
dᵢ ≈ 0.617 m

Therefore, the image is located approximately 0.617 meters away from the lens.