Measuring n Using a PrismAlthough we do not prove it here, the minimum angle of deviation &min for a prism occurs when the angle of incidence 0, is suchthat the refracted ray inside the prism makes the same angle with the normal to the two prism faces as shown in the figure.Obtain an expression for the index of refraction of the prism material in terms of the minimum angle of deviation and the apexangle 0.Ф2k8minA light ray passing through a prism at the minimum angle of deviation 6min:SOLUTIONConceptualize Study the figure carefully and be sure you understand why the light ray comes out of the prism traveling ina differentdirection.Categorize In this example, light enters a material through one surface and leaves the material at another surface. Let's applythe wave under refractionv model to the light passing through the prism.AnalyzeФConsider the geometry in the figure, where we have used symmetry to label several angles. The reproduction of the angleat2the location of the incoming light ray shows that 0, =ФThe theorem that an exterior angle of any triangle equals the sum ofthe two opposite interior angles shows that ômin = 2a. The geometry also shows the following (Use the following as necessary: 0,and a.):,- 2()Combine these three geometric results (Use the following as necessary: 0 and &min):®1 = 02 + a =Apply the wave under refraction model at the left surface and solve for n (Use the following as necessary: 0, and 0,):(1.00)sin(0,) = nsin(0,) - n =Substitute for the incident and refracted angles (Use the following as necessary: 0 and 8min:):n =Finalize Knowing the apex angle O of the prism and measuring 8mint you can calculate the --Select---- of the prismmaterial. Furthermore, a hollow prism can be used to determine the values of n for various liquids filling the prism.EXERCISEA prism with index of refraction of 1.74 has an apex angle of 50.0°. What is the angle of minimum deviation (in degrees) of alight beam through this prism?HintNeed Help?Read It

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Measuring n Using a Prism Although we do not prove it here, the minimum angle of deviation 6min for a prism occurs when the angle of incidence 0, is such that the refracted ray inside the prism makes the same angle with the normal to the two prism faces as shown in the figure. Obtain an expression for the index of refraction of the prism material in terms of the minimum angle of deviation and the apex angle 0. A light ray passing through a prism at the minimum angle of deviation 6in SOLUTION Conceptualize Study the figure carefully and be sure you understand why the light ray comes out of the prism traveling in a different v direction. Categorize In this example, light enters a material through one surface and leaves the material at another surface. Let's apply the wave under refraction model to the light passing through the prism. Analyze Consider the geometry in the figure, where we have used symmetry to label several angles. The reproduction of the angle. at Ф The theorem that an exterior angle of any triangle equals the sum of 2 the location of the incoming light ray shows that 0, = the two opposite interior angles shows that ômin = 2a. The geometry also shows the following (Use the following as necessary: 0, and a.): Combine these three geometric results (Use the following as necessary: 0 and 6min): 0 = 02 + a = Apply the wave under refraction model at the left surface and solve for n (Use the following as necessary: 0, and 0,): (1.00)sin(@,) = nsin(0,) →n = Substitute for the incident and refracted angles (Use the following as necessary: 0 and &min:): Finalize Knowing the apex angle o of the prism and measuring 6minr you can calculate the -Select-- - of the prism material. Furthermore, a hollow prism can be used to determine the values of for various liquids filling the prism. EXERCISE A prism with index of refraction of 1.74 has an apex angle of 50.0°. What is the angle of minimum deviation (in degrees) of a light beam through this prism? Hint