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Define wavefront. Draw the shape of refracted wavefront when the plane incident wave undergoes refraction from optically denser medium to rarer medium. Hence prove Snell’s law of refraction.Β 

Answer

A locus of points in space which oscillate in the same phase is called a wavefront .Β 

That is, the phase difference between any two points of the same wavefront is zero .

Let us assume an incident wavefront AB incident on an interface between 2 media with refraction indices n1>n2.

PROOF OF SNELL'S LAW USING HUYGEN'S WAVE THEORY.jpg

According to Huygen’s wave theory:

  • A source of lightΒ  gives out waves in all directions.
  • Every point on the wavefront is a source of disturbance. These disturbances called secondary wavelets,Β  travel in all directions.
  • The time taken by secondary wavelets to travel from primary to secondary wavefront is a constant .Β 

Therefore, on the basis on these statements we can say that:

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Β 

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Transcript

Question 7 Define wavefront. Draw the shape of refracted wavefront when the plane incident wave undergoes refraction from optically denser medium to rarer medium. Hence prove Snell’s law of refraction. The time taken by the wavefront to travel Distance BC and AE in the same 𝑑_𝐡𝐢=𝑑_𝐴𝐸 If the velocity of the wave front in medium 1 and 2 is 𝑣_1 and 𝑣_2 𝑑_𝐡𝐢=𝑑_𝐴𝐸 𝐡𝐢/𝑣_1 = 𝐴𝐸/𝑣_2 𝐡𝐢/(𝑐/𝑛_1 )=𝐴𝐸/(𝑐/𝑛_2 ) γ€–(𝑛〗_1) 𝐡𝐢=γ€–(𝑛〗_2) 𝐴𝐸 𝑛_1/𝑛_2 =𝐴𝐸/𝐡𝐢 Now, sin⁑𝑖=𝐡𝐢/𝐴𝐢, sinβ‘π‘Ÿ=𝐴𝐸/𝐴𝐢 sinβ‘π‘Ÿ/sin⁑𝑖 = ((𝐴𝐸/𝐴𝐢))/((𝐡𝐢/𝐴𝐢) )=𝐴𝐸/𝐡𝐢=𝑛_1/𝑛_2 sinβ‘π‘Ÿ/sin⁑𝑖 =𝑛_1/𝑛_2 𝑛_2 sinβ‘π‘Ÿ=𝑛_1 sin⁑𝑖 Or 𝑛_1 sin⁑𝑖=𝑛_2 sinβ‘π‘Ÿ Hence, snells law is proved using huygen’s wave theory.

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.