Let some unpolarised light is travelling along X-axis. Its electric field will be randomly oriented on Y-Z plane. We can represent this unpolarised light in terms of two components of electric field along Y-axis and Z-axis respectively and these two components are assumed to be at a phase difference. Thus
`E_y = E_1 sin(omega t - kx)`
`E_z = E_2 sin (omega t - k x + delta)`
If value of `delta` changes randomly with time, then light is said to be unpolarised.
If value of `delta` is such that tip of the resultant electric field traces a straight line, then light is said to be linearly polarised. Similarly for circular path, light is said to be circularly polarised and for elliptical path, light is said to be elloptically polarised.
Light will be linearly polarised if

Options

A. `delta = 0`
B. `delta = pi`
C. `delta = pi//2`
D. `delta = pi//4`

Answer

A, B

Explanation

If resultant electric field makes an angle `theta` with the Y-axis, then
`tan theta = (E_2)/(E_y)`
For `delta = 0` and `pi` we can see that `tan theta` remains constant and hence tip of the net electric field traces a straight line. So we can say that for `delta = 0 and pi` light will be linearly polarised.