In one of the experiments, two convex lenses with focal lengths f_1 and f_2 were
ID: 2077624 • Letter: I
Question
In one of the experiments, two convex lenses with focal lengths f_1 and f_2 were placed in contact on a single component carrier. This combination of lenses was used to produce an image on the screen of the filament of the light bulb inside the incandescent light source. The distance between the carrier and the filament o was varied. For each value of o, the position of the screen was adjusted to obtain a clear image of the filament. The distance between the lenses and the screen i was recorded. For the recorded data, 1/i was plotted vs 1/o. (a) The equation of the plotted line is 1/i = -1.11 1/o + 0.0135 If i and o were recorded in mm, what is the focal length of this combination of lenses? (b) The uncertainty in the slope is 0.013 and the uncertainty in the y intercept is 0.00012 mm^-1. What is the uncertainty in the focal length of this lens combination? You must use calculus for full credit. (c) Report the focal length of this lens combination as f plusminus sigma_f.Explanation / Answer
lens formula
1/v - 1/u = 1/f , v is the image distance and u is the object distance measure from thecenter of the lens. distances measured in the directionof light are +ve , the sign convention.
for Convex lens u is -ve
in our problem u =o and i = v
the eq. 1/i = -1.11 *1/o + 0.0135 represents the lens formula
the intercept 0.0135 is 1/f
the focal lenth of the combination lens = 1/0.0135 mm = 74.07 mm
b) the focal length is related to the intercept
uncertianity in intercept = 0.00012 /mm
uncertianity % in 1/ f = 0.00012/0.0135 = 0.89%
uncertainity if f = 74.07*0.0089 =0.658 mm
c)focal length of the lens combination f = 74.07 +/- 0.658 mm
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