Question

snells law derivation

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Answer 1

Answer:

Let’s derive Snell’s law formula using Fermat’s principle. Fermat’s principle states that “light travels in the shortest path that takes the least time”.

Snell’s Law FormulaLet the refractive index of medium 1 and medium 2 are n1 and n2 respectively. Light enters from medium 1 to medium 2 through the point O. Here, θ1 is the angle of incidence; θ2 is the angle of refraction.

The traveling velocities of light in medium 1 and medium 2 are given by:

v1=cn1

v2=cn2

Where ‘c’ is the speed of light in vacuum

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

T=x2+a2√v1+b2+(1−x2)v2

dTdx=xv1x2+a2√+−(1−x)v2b2+(1−x2)√

=0—————— (1)

xx2+a2√+sinθ1

Substitute the values in equation 1, we get

dTdx=sinθ1v1+sinθ2v2=0

sinθ1v1=sinθ2v2

Substitute the values of v1 and v2,

n1sinθ1c=n2sinθ2c

n1sinθ1=n2sinθ2

Hence proved