Explain what is optical path length. How is it different from actual path length?

What is the shape of the wavefront in each of the following cases:

(a) Light diverging from a point source.

Define optical path and prove that optical path $\left(\mathrm{\Delta }\right)=\mathrm{nd}$, where $\mathrm{n}$ is the refractive index of medium other than the air and ‘$\mathrm{d}$’ is the distance travelled in the medium. If a mica sheet of thickness ‘$\mathrm{t}$’ and refractive index ‘$\mathrm{n}$’ is placed in the path of a ray of light, by how much the optical path is included?

A high-powered laser beam $(\lambda =600 \mathrm{nm})$ with a beam diameter of $10 \mathrm{cm}$ is aimed at the Moon, $3.8\times {10}^5 \mathrm{km}$ distant. The beam spreads only because of diffraction. The angular location of the edge of the central diffraction disk is given by

$\mathrm{sin\theta }=\frac{1.22\lambda }{d}$

where $d$ is the diameter of the beam aperture. What is the diameter of the central diffraction disk on the Moon's surface?