Light is indeed a transverse wave, and its ability to propagate without a medium is a characteristic of electromagnetic waves. Let me explain in more detail.
A transverse wave is one in which the oscillations of the wave occur perpendicular to the direction of wave propagation. In the case of light, it is an electromagnetic wave consisting of oscillating electric and magnetic fields.
When light propagates through a medium such as air or water, it interacts with the atoms or molecules in that medium, causing them to oscillate and transfer the energy of the wave. This interaction gives rise to phenomena like refraction and reflection.
However, light can also propagate through a vacuum, such as outer space, where there is no material medium. In this case, the electric and magnetic fields self-propagate through space without the need for a medium to transfer the energy. This is due to the nature of electromagnetic fields.
According to Maxwell's equations, which describe the behavior of electromagnetic fields, changing electric fields give rise to magnetic fields and changing magnetic fields give rise to electric fields. This self-sustaining process allows the electromagnetic wave to propagate through space without relying on a material medium.
In summary, light is a transverse wave because its electric and magnetic fields oscillate perpendicular to the direction of wave propagation. While many waves require a material medium to propagate, light can travel through a vacuum because it is an electromagnetic wave, and its electric and magnetic fields can self-propagate through space.