6. When a ray of light travels from one medium to another, it changes direction. This phenomenon isknown as refraction. In the figure below, light is traveling from A to B. The amount of refractiondepends on the velocities vi and v2, of light in the two media and on Fermat's Principle which statesthat the light's time of travel, T, from A to B, is a minimum(a) Find an expression for T in terms of x and the constants a, b, v1, v2 and c.(b) Show that if R is chosen so that the time of travel is minimized, thensin 01sin 02This result is known as Snell's Law and the ratio v1/v2 is called the index of refraction of thesecond medium with respect to the first medium. (Suggestion: Calculate set 0 but donot solve for x. Use this final equation to directly calculate the fraction Medium 1Velocity1A01RB'-C--Medium 2BVelocity 2CFigure 2: Snell's Law

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Asked Nov 20, 2019
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6. When a ray of light travels from one medium to another, it changes direction. This phenomenon is
known as refraction. In the figure below, light is traveling from A to B. The amount of refraction
depends on the velocities vi and v2, of light in the two media and on Fermat's Principle which states
that the light's time of travel, T, from A to B, is a minimum
(a) Find an expression for T in terms of x and the constants a, b, v1, v2 and c.
(b) Show that if R is chosen so that the time of travel is minimized, then
sin 01
sin 02
This result is known as Snell's Law and the ratio v1/v2 is called the index of refraction of the
second medium with respect to the first medium. (Suggestion: Calculate set 0 but do
not solve for x. Use this final equation to directly calculate the fraction
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6. When a ray of light travels from one medium to another, it changes direction. This phenomenon is known as refraction. In the figure below, light is traveling from A to B. The amount of refraction depends on the velocities vi and v2, of light in the two media and on Fermat's Principle which states that the light's time of travel, T, from A to B, is a minimum (a) Find an expression for T in terms of x and the constants a, b, v1, v2 and c. (b) Show that if R is chosen so that the time of travel is minimized, then sin 01 sin 02 This result is known as Snell's Law and the ratio v1/v2 is called the index of refraction of the second medium with respect to the first medium. (Suggestion: Calculate set 0 but do not solve for x. Use this final equation to directly calculate the fraction

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Medium 1
Velocity1
A
01R
B'
-C--
Medium 2
B
Velocity 2
C
Figure 2: Snell's Law
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Medium 1 Velocity1 A 01R B' -C-- Medium 2 B Velocity 2 C Figure 2: Snell's Law

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Expert Answer

Step 1
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Part la) Tn medliam 1 velocity is V ard olisplacement ia-) Simidary n medium 2 veloc V and displacement i tb at Cen C-X

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Step 2
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T2 (ime med fum2) TTotal fime=T(time in medlum 1) + diaplacement velocit Time at(n T = VI

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Step 3
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Part (8) x2 b2 Ja (e- 2. T= Totel time, VZ and a fanction af ince time Lonatants a, b V2and C o minimige , one can alifferentiete dT dn

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