Question
You measure three segments of the distance between a diffraction slit an the screen on which the pattern forms: x1 = (11.0 - 0.2) cm, x2 = (6.2 +0.4) cm, and x3 = (16.3 + 0.2). What is the uncertainty of the total distance x1 + x2 + x3? 0.5 cm O 0.7 cm 0.8 cm 0.9 cm O 0.6 cm
Answer
0.6 cm
- Q: What is the formula for the propagation of uncertainty? A: The formula is δf = √(δf1)² + (δf2)² + ... + (δfn)², where δf is the uncertainty of the final value, δf1, δf2, ..., δfn are the uncertainties of the individual values.
- Q: What are the uncertainties of x1, x2, and x3? A: δx1 = 0.2 cm, δx2 = 0.4 cm, δx3 = 0.2 cm.
- Q: What is the total distance x1 + x2 + x3? A: x1 + x2 + x3 = (11.0 - 0.2) cm + (6.2 +0.4) cm + (16.3 + 0.2) cm = 33.9 cm.
- Q: What is the uncertainty of x1 + x2 + x3? A: δ(x1 + x2 + x3) = √(δx1)² + (δx2)² + (δx3)² = √(0.2)² + (0.4)² + (0.2)² = 0.6 cm.