A monochromatic beam of light has a frequency `v = 3/(2pi) xx 10^(12) Hz` and is propagating along the direction `(hati + hatj)/(sqrt(2))`. It is polarizied along the `hatk` direction. The accpetable fromfor the magnetic field is :

Options

A. `(E_0 )/(C ) ((hati - hatj )/( sqrt(2))) cos [ ((hati - hatj ))/(sqrt(2)) vecr - ( 3xx 10^(12) )t ]`
B. `(E_0 )/(C ) hatk cos [ 10^4 ((hati - hatj ))/( sqrt(2)), vecr + ( 3 xx 10^(12) )t ]`
C. `(E_0 )/(C ) ((hati + hatj )/( sqrt(2))) cos [ 10 ^4 ((hati + hatj ))/( sqrt(2)) .. Vecr + (3 xx 10^(12) t)]`
D. `(E_0 )/(C ) ( ( hati + hatj + hatk )/( sqrt(3))) cos [ 10^4 ((hati + hatj ))/( sqrt(2)) . Vecr +(3 xx 10^(12) ) t ]`

Answer

C

Explanation

`hatE xx hatB` should give direction of wave propgation wave is polarised along z - axis hence ` hatE ` must be along `hatk `
` c= (1)/ sqrt( mu _0 epsi_0 ) or v =(1)/( sqrt( mu epsi))implies v lamda = (1 )/( sqrt(mu epsi_0))`
` = > hatk xx hatB || ( hati + hatj)/( sqrt(2))`
option -(a) ` hatk xx (hati - hatj ) /( sqrt(2)) = ( hatj - (-hati))/( sqrt(2))= ( hati + hatj )/( sqrt(2) ) || ( hati + hatj )/( sqrt(2))`
option - (b) and (d) do not satisfy this
wave propagation vector `hatk ` should be along `( hati + hatj )/( sqrt(2))`
So correct option is (c ) .