- #1

songoku

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- Homework Statement
- The equation connecting object distance u, image distance v and focal length f for a lens is 1/u +1/v = 1/f . A student measures values of u and v, with their associated uncertainties. These are

u = 50 mm ± 3 mm and v = 200 mm ± 5 mm. He calculates the value of f as 40 mm. What is the uncertainty in this value?

A ±2.1 mm

B ±3.4 mm

C ±4.5 mm

D ±6.8 mm

- Relevant Equations
- Percentage and absolute uncertainty

##\frac{1}{f}=\frac{1}{u}+\frac{1}{v}##

##f = \frac{u.v}{u+v}##

Let: u + v = w → w = 250 mm ± 8 mm

Percentage uncertainy of v = (3/50) . 100% = 6%

Percentage uncertainty of u = (5/200) . 100%=2.5%

Percentage uncertainty of w = (8/250) . 100% = 3.2%

Percentage uncertainty of f = 6 % + 2.5 % + 3.2 % = 11.7 %

Absolute uncertainty of f = 11.7 % x 40 = 4.68 mm

But the answer should be A

Where is my mistake? Thanks

##f = \frac{u.v}{u+v}##

Let: u + v = w → w = 250 mm ± 8 mm

Percentage uncertainy of v = (3/50) . 100% = 6%

Percentage uncertainty of u = (5/200) . 100%=2.5%

Percentage uncertainty of w = (8/250) . 100% = 3.2%

Percentage uncertainty of f = 6 % + 2.5 % + 3.2 % = 11.7 %

Absolute uncertainty of f = 11.7 % x 40 = 4.68 mm

But the answer should be A

Where is my mistake? Thanks