With a focal length of 10 cm, and D zero is 20, 15, 25, and 5, what is the D one
To find D₁ (the distance of the object from the lens), we can use the lens formula, which is:
1/f = 1/D₀ + 1/D₁
Where:
f = focal length of the lens
D₀ = distance of the image from the lens
Given a focal length of 10 cm (f = 10 cm) and D₀ values of 20 cm, 15 cm, 25 cm, and 5 cm, we can substitute these values into the lens formula to find D₁ for each case.
Case 1: D₀ = 20 cm
1/10 = 1/20 + 1/D₁
Simplifying the equation:
1/10 = 2/40 + 1/D₁
1/10 = 1/20 + 1/D₁
Multiplying through by 20D₁:
2D₁ = D₁ + 20
D₁ = 20 cm
So, in this case, when D₀ is 20 cm, D₁ is also 20 cm.
Case 2: D₀ = 15 cm
1/10 = 1/15 + 1/D₁
Multiplying through by 15D₁:
1.5D₁ = D₁ + 15
0.5D₁ = 15
D₁ = 30 cm
So, in this case, when D₀ is 15 cm, D₁ is 30 cm.
Case 3: D₀ = 25 cm
1/10 = 1/25 + 1/D₁
Multiplying through by 25D₁:
2.5D₁ = D₁ + 25
1.5D₁ = 25
D₁ = 16.67 cm (rounded to two decimal places)
So, in this case, when D₀ is 25 cm, D₁ is approximately 16.67 cm.
Case 4: D₀ = 5 cm
1/10 = 1/5 + 1/D₁
Multiplying through by 5D₁:
0.5D₁ = D₁ + 5
-0.5D₁ = 5
D₁ = -10 cm
In this case, when D₀ is 5 cm, D₁ is -10 cm. However, negative distances do not make physical sense in the context of lenses and optics. Therefore, we can ignore this solution.
To summarize:
- When D₀ is 20 cm, D₁ is 20 cm.
- When D₀ is 15 cm, D₁ is 30 cm.
- When D₀ is 25 cm, D₁ is approximately 16.67 cm.