Mathematical Explanation:
When two linearly polarized lights with a phase difference of π/2 are combined, they can create circularly polarized light. Let's consider two linearly polarized waves with the same amplitude and frequency, but with a phase difference of π/2:

E₁ = E₀cos(ωt)
E₂ = E₀cos(ωt + π/2)

Here, E₀ represents the amplitude of the waves, ω is the angular frequency, and t is the time. The electric field of the resulting circularly polarized wave can be represented as:

E_cpl = E₁ + E₂
= E₀cos(ωt) + E₀cos(ωt + π/2)
= E₀cos(ωt) + E₀sin(ωt)
= E₀(cos(ωt) + sin(ωt))

This can be further simplified using the trigonometric identity cos(θ) + sin(θ) = √2sin(ωt + π/4):

E_cpl = E₀√2sin(ωt + π/4)

Diagrammatic Explanation:
To understand the concept visually, we can represent the two linearly polarized waves on the x and y axes of a coordinate system. The x-axis represents the electric field in the horizontal direction, and the y-axis represents the electric field in the vertical direction.

1. Draw a coordinate system with the x and y axes.
2. On the x-axis, represent the electric field of the first linearly polarized wave (E₁ = E₀cos(ωt)).
3. On the y-axis, represent the electric field of the second linearly polarized wave (E₂ = E₀cos(ωt + π/2)).
4. At any given time, the sum of the electric fields on the x and y axes represents the resulting electric field at that time.
5. As the waves oscillate, the resulting electric field traces a circular path in the coordinate system, creating a circularly polarized wave.

This diagram visually demonstrates how the combination of two linearly polarized waves with a phase difference of π/2 produces circularly polarized light.

Summary:
When two linearly polarized lights with a phase difference of π/2 are combined, the resulting electric field can be represented mathematically as E_cpl = E₀√2sin(ωt + π/4). Visually, the combination of these waves creates a circularly polarized wave, as represented by a circular path in a coordinate system.