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Question

The incident ray, reflected ray, and the outward drawn normal are denoted by the unit vectorsa,b and c. Respectively. Then choose the correct relation for these vectors.


A

b=2a+c

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B

b=a-c

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C

b=a+2c

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D

b=a-2a·cc

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Solution

The correct option is D

b=a-2a·cc


The explanation for the correct option:

In the case of option D,

  1. The incident ray, reflected ray, and the outward drawn normal are denoted by the unit vectorsa,b andc.
  2. From the law of refraction, i=r let i=r=θ
  3. From figure, a=sinθi^-cosθj^b=sinθi^+cosθj^c=j^
  4. Now take option D

=a-2a·cc=sinθi^-cosθj^-2sinθi^-cosθj^.j^j^=sinθi^-cosθj^-2-cosθj^=sinθi^-cosθj^+2cosθj^=sinθi^+cosθj^=b

Therefore the correct relation is b=a-2a·cc

The explanation for the incorrect option:

In the case of option A,

  1. Take option A, b=2a+c
  2. On further solving=2a+c=2sinθi^-cosθj^j^=2-cosθb
  3. Not correct relation

In the case of option B,

  1. Take b=a-c
  2. On further solving, =a-c=sinθi^-cosθj^-j^=sinθ-1+cosθj^b
  3. Not correct relation.

In the case of option C,

  1. Similarly, take b=a+2c
  2. On Further solving, =a+2c=sinθi^-cosθj^+2j^=sinθi^-j^cosθ-2b
  3. Not correct relation.

Hence, option D is the correct answer.


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