Through the equation n1 sin θ1 = n2 sin θ2, the Snell’slaw relates the incident angle θ1 of a ray traveling in amedium of index n1 to the refraction angle θ2 of the samelight ray in the medium of refraction index n2. Find n2 andits uncertainty from the following measurementsθ1 = 22.0◦ ± 0.2◦θ2 = 16.3◦ ± 0.2◦n1 = 1.000 (assumed to be exact)Note that δθ must be converted into radians when youcompute the uncertainty. In calculus, we only use radiansin trigonometrical functions

Laser light from the Doppler sensor travels through air with a refractive index of n1 and into a glass block at an incident angle of θ1.  The refractive index of the glass block is n2, and the angle of refraction is θ2.  What is the ratio of n1 to n2?A.θ2θ1θ2θ1B.sinθ2sinθ1sinθ2sinθ1C.θ1θ2θ1θ2D.sinθ1sinθ2

A ray of light is incident normally on one of the faces of a prism of apex angle 30° and refractive index 2√. The angle of deviation of the ray is

Let us first define the standard deviation s. Suppose weperform N measurements 1, 2, · · · , N with the average¯. Then the deviation of each measurement is given byδ =  − ¯ with  = 1, 2, · · · , N. The standard deviation s iss =√√√ ∑N=1(δ)2N − 1When we report the average value of N measurements,the uncertainty we should associate with this averagevalue is the standard error.σ = spN =√√√√∑N=1(δ)2N(N − 1)The standard error is smaller than the standard deviationby a factor of 1/pN, since the statistical uncertainty canbe reduced by large number of measurements. Also it isuseful to write σ2 = δ2 ≡ 1N(N − 1)N∑=1δ2 .Suppose we want to determine a quantity  = ƒ (, ),which depends on  and . We want to know the error in = ƒ (, ) if we measure  and  with errors σ and σ .Using the Taylor expansion, we can obtain the law of theerror propagation as follows(δ)2 = ∂ƒ∂2(δ)2 + ∂ƒ∂2(δ)2 + 2 ∂ƒ∂∂ƒ∂(δδ)If the measurements of  and  are uncorrelated, then,on the average, we should expect to find equal distribu-tions of positive and negative values for this term, and weshould expect (δδ) = 0. At the end of the day, using thedefinition of the standard error σ, we can obtainσ =√√√ ∂ƒ∂2σ2 + ∂ƒ∂2σ2Exercise problems: Now find the standard error σ in = ƒ (, ) as a function of the errors in σ and σ for thefollowing functions:(a)  =  +  (0.5 pts)You can find the absolute uncertainty of the sum(or difference) is the root square sum of theindividual absolute uncertainties when adding (orsubtracting).(b)  =  ×  (0.5 pts)(c)  = /  (1 pt)You can find that the relative uncertainty of the prod-uct (quotient) is the root square sum of the individualrelative uncertainties.(d)  = 2 (1 pt)(e)  =  exp(c) with c constant. (0.5 pts)(f)  = 1/ 

In part A of the experiment a pair of slits are illuminated with a laser and an interference pattern is observed. The slit spacing is d = (0.100 ± 0.003) mm and the pattern is projected on to the wall a distance L= (2.352 ± 0.02) m from the slits. From a dark spot 8 further dark spots are counted and the distance is measured to be Z = (12.2 ± 0.4) cm.The wavelength of the laser is calculated to be λ = 648 nm.Calculate the uncertainty in the wavelength. Express answer in nm (1x10-9m) to the nearest whole number.

In part A of the experiment a pair of slits are illuminated with a laser and an interference pattern is observed. The slit spacing is d = (0.100 ± 0.003) mm and the pattern is projected on to the wall a distance L= (2.352 ± 0.006) m from the slits. From a dark spot 8 further dark spots are counted and the distance is measured to be Z = (12.2 ± 0.9) cm.The wavelength of the laser is calculated to be λ = 648 nm.Calculate the uncertainty in the wavelength. Express answer in nm (1x10-9m) to the nearest whole number.