A laboratory group measures the dimensions and placement of an arrow in front of a…

PHYSICS · Multi-part · CBSE · Physics · Light — Reflection and Refraction · Light — Reflection and Refraction

Problem

A laboratory group measures the dimensions and placement of an arrow in front of a concave spherical mirror. Their data (with estimated uncertainties) are recorded below. • Object height:

h_{o}=\left(2.50\;\pm\;0.05\right)\text{ cm}

• Image height:

h_{i}=\left(-0.75\;\pm\;0.02\right)\text{ cm}

(negative sign indicates inversion) • Object distance:

s_{o}=\left(28.0\;\pm\;0.3\right)\text{ cm}

Using these data, complete all tasks. Express final numerical answers with the correct number of significant figures and absolute uncertainties. (a) Derive an algebraic expression for the mirror’s focal length

f

in terms of

h_{o}

h_{i}

, and

s_{o}

only (eliminate the image distance symbolically). (b) Use the measured values to calculate the numerical value of the focal length. (c) Propagate the given measurement uncertainties to determine the absolute uncertainty in

f

. Clearly state any assumptions made in your propagation method. (d) Report the focal length with its uncertainty in the standard form

f\;=\;\text{value}\;\pm\;\text{uncertainty}\;\text{cm}

and briefly comment on the dominant source of error.

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