Assume you have measured your little metal sphere's diameter to be 2.500 ± 0.005 cm and its mass to be 63.00 ± 0.05 g.

Physics

1 answer:

TiliK225 [7]2 years ago

5 0

Answer:

V = (8.2 ± 0.1) cm³ , % = 1.2%

Explanation:

The volume of the sphere is

V = 4/3 π r³

The error in volume is

ΔV = 4 / 3 π r² Δr

DV = 4 π r² Δr

Let's calculate

V = 4/3 π (2.500 / 2)³

V = 8,181 cm³

ΔV = 4 π 2,500²/4 0.005

ΔV = 0.098 cm³

V = (8.2 ± 0.1) cm³

The equation for the percentage error is

% = ΔV / V 100

% = 0.1 / 8.2 100

% = 1.2%

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How do your results from ray tracing compare to your results from using the thin-lens equation?

EastWind [94]

Answer:

20cm

Explanation:

A convex lens has a positive focal length and the object placed in front of it produce both virtual and real image <em>(image distance can be negative or positive depending on the nature of the image</em>).

According to the lens equation

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$ where;

f is the focal length of the lens

u is the object distance

v is the image distance

If the magnification is - 0.6

mag = v/u = -0.5

v = -0.5u

since v = 10cm

10 = -0.5u

u = -10/0.5

u =-20 cm

Substitute u = -20cm ( due to negative magnification)and v = 10cm into the lens formula to get the focal length f

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\\\frac{1}{f} = \frac{1}{-20} + \frac{1}{10}\\\frac{1}{f} = \frac{1}{-20} + \frac{1}{10}\\\frac{1}{f} = \frac{-1+2}{20} \\\frac{1}{f} = \frac{1}{20} \\cross \ multiply\\f = 20\\f = 20 cm$