Can someone explain optical path difference?

Ok so the definition seems to be is the distance a wave would travel in air in the same time as it travelled in another medium.

But I don't understand why the formula is then opd=refractive index*geometrical path difference ??

Refractive index $n = \frac{c}{v}$

Where c is the speed of light in a vacuum and v is the velocity through the medium.

Optical path length is defined as the product of the refractive index and the geometrical distance the light travels.

$\mathrm {opl} = nd$

Optical path difference is a way of describing the phase shift between two paths emanating from the same coherent light source arriving at the same point after propagating different lengths and/or different mediums.

$\mathrm {opd} = n_{1}d_{1} - n_{2}d_{2}$


If the same medium is propagated in both cases then the refractive index is common and can be taken outside brackets:

$\mathrm {if} \ n = n_1 = n_2$

then

$\mathrm {opd} = n_{1}d_{1} - n_{2}d_{2} = n(d_{1} - d_{2})$