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Question

If ^i denotes a unit vector along an incident ray, ^r a unit vector along the refracted ray into a medium of refractive index 'μ' and ^n a unit vector normal to the boundary of the media directed towards the incident medium, then
[consider the first medium to be air]

A
^i.^n=μ(^r.^n)
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B
^i×^n=μ(^n×^r)
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C
^i×^n=μ(^r×^n)
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D
μ(^i×^n)=^r×^n
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Solution

The correct option is C ^i×^n=μ(^r×^n)
As per given conditions,

^i be the unit vector along the incident ray.
^r be the unit vector along the refracted ray.
^n is the unit vector along normal to the interface of two medium.
Applying Snell's law,
μ1sini=μ2sinr
1×sin(180i)=μsin(180r)
|^i||^n|sin(180i)=μ(|^r||^n|sin(180r))
^i×^n=μ(^r×^n)
Why this question?
Caution: Magnitude wise (^r×^n) and (^n×^r) will yield the same. However, the direction of (^i×^n) will be opposite to the direction of (^n×^r).

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