ATION AND REFRACTION OF PERIODIC WAVES he c as it ropagates from a mediunm malle

Question

ATION AND REFRACTION OF PERIODIC WAVES he c as it ropagates from a mediunm maller wave speed. a mahematical OPAGATION AND REFRACTION lingram at right illustrates refraction ger wave speed to a medium of Name Waves HW-123 the relationship between Larget Larger wave speed the angle of incidence (', the angle Smaller wave speed of refraction (U, the wavelength of Smaller the incident wave fa), and the the iheri facted wave (au) Show your work. Starting from the equation that you wrote above. derive a mathematical formula relating 9, Starting from the 6, and where t, and v, are the speeds of the incident and refracted wave,respectively Show your work. b. c. Suppose the speed of the refracted wave were half that of the incident wave. Determine tho angle of refraction for the following angles of incidence: 10°,20.40°, and 80 Does the an L Would the a neliuane relationship that you developed in parts a and b alo sply to a wave pesing from ter S cation nor, CPrentice Hall, Inc. Fint Edition, 2002 tment of

Explanation / Answer

1)it is derived using fermat principle.

assume the refractive index of medium 1 and medium 2 are [n1] and [n2] respectively. Light enters medium 2 from medium 1 via point O.

[theta1] is the angle of incidence, [theta2] is the angle of refraction.

The traveling velocities of light in medium 1 and medium 2 are

[v1=c/n1] and
[v2=c/n2] respectively.

[c] is the speed of light in vacuum.

Let T be the time required for the light to travel from point Q to point P.

[T=rac{sqrt{x^2 + a^2}}{v1} + rac{sqrt{b^2 + (l - x)^2}}{v2}]

[rac{dT}{dx}=rac{x}{v1sqrt{x^2 + a^2}} + rac{ - (l - x)}{v2sqrt{(l-x)^2 + b^2}}=0] (stationary point)

Note that [rac{x}{sqrt{x^2 + a^2}} =sin theta1]

[rac{ l - x}{sqrt{(l-x)^2 + b^2}}=sin theta2]

[frac{dT}{dx}=frac{sin theta1}{v1} - frac{sin theta2}{v2}=0]

[{n1*sin theta1}*{c}={n2*sin theta2}*{c}]

[n1*sin theta1=n2*sin theta2]

2)sin thetha1/sin thetha2= n2/n1=c*v1/c*v2=v1/v2

3) v2=v1/2

when thetha1=10°

Sin10/sin thetha2= v1/(v1/2)

a)Sin thetha2=2/sin10=11.51

b)sin thetha2=2/sin20=5.85

c)sin thetha2=2/sin40=3.11

d)sin thetha2=2/sin 80=2.03

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