to verify law of reflection and refraction using Fermat principle how to perform this experiment with observations
Answers
Answer:
The angle ACB = Θ is a constant angle. But the angle ∠ ACN= θ varies if the point of incidence N changes. = 0 ⇒ y = f2(θ) = stationary. So the Fermat's principle is proved for refraction on a curved surface.
Explanation:
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Answer:
Fermat’s principle states that “light travels between two points along the path
that requires the least time, as compared to other nearby paths.” From Fermat’s
principle, one can derive (a) the law of reflection [the angle of incidence is equal
to the angle of reflection] and (b) the law of refraction [Snell’s law]. This is
problem 32-81 on page 864 of Giancoli. The derivations are given below.
(a) Consider the light ray shown in the figure. A ray of
light starting at point A reflects off the surface at point P
before arriving at point B, a horizontal distance l from
point A. We calculate the length of each path and divide
the length by the speed of light to determine the time
required for the light to travel between the two points.
Derivation of the laws of reflection and refraction
( )
2 2 2 2
1 2 x h x h
t
c c
+ − +
= +
l
To minimize the time we set the derivative of the time with respect to x equal to
zero. We also use the definition of the sine as opposite side over hypotenuse to
relate the lengths to the angles of incidence and reflection.
( )
( )
( )
( )
2 2 2 2
1 2
1 2 12 2 2 2 2
1 2
0
sin sin
dt x x
dx cx h c xh
x x
x h x h
θ θ θθ
− − = =+ →
+ − +
− = → = →=
+ − +
l
l
l
l
1 h 2 h
x l − x