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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(180∘−i)=μsin(180∘−r) ⇒|^i||^n|sin(180∘−i)=μ(|^r||^n|sin(180∘−r)) ⇒^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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