During a laboratory exercise

PHYSICS · Subjective · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

During a laboratory exercise, students measure the angles of incidence and refraction for a light ray passing from air into a transparent plastic block. The measured values (with their uncertainties) are: Angle of incidence:

i = 50.0^{\circ} \pm 0.5^{\circ}

Angle of refraction:

r = 30.0^{\circ} \pm 0.5^{\circ}

(a) Write an expression for the refractive index of the plastic with respect to air in terms of

i

and

r

. (b) Calculate the refractive index using the central values of

i

and

r

. (c) Derive a formula for the fractional uncertainty in the refractive index in terms of the fractional uncertainties in

\sin i

and

\sin r

. (d) Using the given angular uncertainties, determine the absolute uncertainty in the calculated refractive index. Quote your final answer in the form

n \pm \Delta n

. (e) Explain briefly why reducing the angular uncertainty becomes increasingly important when the angles involved are close to

0^{\circ}

90^{\circ}

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