Question

Use a curve fit to determine a value for the index of refraction for the acrylic lens (n2​). Assume that the index of refraction for air (n1​) is 1. Record the experimental value of n2 ​with uncertainty.

Incident Angle 01 (degrees) Refraction Angle 02 (degrees) 0 Incident vs Refraction 10 y = 0.5964x + 1.2242 R2 = 0.9958 13.5 16.8 uw - oo"" 25.6 28.6 31 33.5 35.5 1 10 20 30 40 50 60 70

Answer 1

Froom Shells law, sin elm - Sin, ng les al seksaction where angles of o, and of case the wenslavetively sofraction and nq and na are the refractive indices of the medium I and medium a. here, medium I is air , ng=1, medium zi's acrylic lens , 02. For small angles, oç14, we can write, Sino 20 Thus, the equation (1) be.comes, The line * (for 0,30,514) curve is plotted between o, and on, which is a straigh with slope , m=0.5964. But slope of the carve 1 (for small angles) m > n = = obec = 1.6767 calculating The uncertainty in n is given by the error in 12 from the core.

Differentiating, MaxINUUT Los a enna = lnn, + dnm » ln n2 = ln n + ln 02 sont comme + 024 go ( form mazinun essos) shine - + S0 ( an, -o, as n, is given, not measured in the experiment) 9 anza na lang ang in) —%) wohers, 402=5 40,= 40 ase lohe minimum value that can be measured certainly in the o, and O2 axes of the graph. (3) on, = 9.6767 * ( 4) Here, 0,, Oz ase the angles at which slope is calculated. But the curve is a straight line, thus slope is same at infinite values of 0,02 . But, we calculated na using the formula , n2 = 0%= slope of the curve, which is valid for only small angles (6., 22 <14). From the experimental data , we can choose, either Q=10, Q = 7 or 0,= 5, 02=4. But the first choise would be more preferable as they are comparable but not smaller 1.676

than the errors no, and aq respectively. Putting, 6,510, 0, +7 in equation (9) one = 1.6767 x ( 16+) = 1.6767x C1+ 0.714) z 1,6767 x 10714 22.874 Thus the experimentally obtained value of nais, (-6767 * 2.874). Thus total uncertainity in ne is 4.676772.874) - (1.6767 – 2.874) = 2x2.874 = .748