A mirror and source of light are situated at the origin O and a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the DRs of the normal to the plane of mirror are `1,-1,1,` then DCs for the reflacted ray are :

Options

A. `(:(1)/(3),(2)/(3),(2)/(3):)`
B. `(:(-1)/(3),(-2)/(3),(2)/(3):)`
C. `(:(-1)/(3),(-2)/(3),(-2)/(3):)`
D. None

Answer

B

Explanation

For B to win:
PR or `overset(RBR)(BR R)`
`{:("Black",,"Red",,"B(n)",,,),(1,,2,,B(1)=1,,,overset(A(n))A(1)=0),(2,,2,,B(2)=(2)/(4).(1)/(3)+(2)/(4).(2)/(3).(1)/(2)+(2)/(4).(2)/(3).(1)/(2),,,),(3,,2,,B(3)=(2)/(5).(1)/(4)+(2)/(5).(3)/(4).(1)/(3)+(3)/(5).(2)/(4).(1)/(3),,,),(n,,2,,B(n)=(2)/(n+2).(1)/(n+1)+(2)/(n+2).(n)/(n+1).(1)/(n)+(n)/(n+2).(2)/(n+2).(1)/(n),,,):}`
`therefore B(n) = (6)/((n+1)(n+2))`
`A(n)=1-B(n)=((n-1)(n+4))/((n+1)(n+2))`
`pi[A(n)]=(6xx(n+2)(n+3)(n+4))/(3xx4xx5.n(n+1)(n+2))`