WBJEE 2024 Physics & Chemistry Paper

The given electric field is:

→

E

(x,y,z,t)=E0

^

n

eiko[(x+y+z)−ct]
We can rewrite this as:

→

E

(x,y,z,t)=E0

^

n

eiko[(

^

i

+

^

j

+

^

k

)⋅

→

r

−ct]

where

→

r

=x

^

i

+y

^

j

+z

^

k

is the position vector. This represents a plane wave propagating in the direction of

^

i

+

^

j

+

^

k

.
The wave vector is given by:

→

k

=ko(

^

i

+

^

j

+

^

k

)

The magnitude of the wave vector is:
k=|

→

k

|=ko√3
The speed of the wave in the medium is given by:
v=‌

ω

k

=‌

cko

ko√3

=‌

c

√3

The refractive index of the medium is given by:
n=‌

c

v

=√3

Since the electric field is polarized in the x−z plane, the polarization vector

^

n

must be a linear combination of

^

i

and

^

k

. To ensure the polarization is in the x−z plane, and considering the wave is propagating along

^

i

+

^

j

+

^

k

, the polarization vector must be perpendicular to the direction of propagation. Thus:

^

n

=‌

^ i − ^ k

√2

Therefore, the correct options are:
Option B:

^

n

=‌

^ i − ^ k

√2

;v=‌

c

√3

.
Option C: Refractive index of the medium is √3.