Physics - Wave Optics Question with Solution | TestHub

Path difference$=\text{BN}+\text{BA}+\frac{\text{λ}}{2}$

(because reflection occurs from denser medium)



In$\Delta \text{ACB}$

$\frac{\mathrm{h}}{\text{AB}}=\text{cos α}$

$\text{AB}=\frac{\mathrm{h}}{\text{cos α}}\text{....(1)}$

from right angle$\Delta \text{ANB}$

$\frac{\text{BN}}{\text{AB}}=\text{cos 2}\text{α}$

$\mathrm{BN}=\mathrm{AB}\cos 2\alpha$....(2)

Path difference$=\left(\text{AB}+\text{AB }\text{cos 2}\text{α}\right)+\frac{\text{λ}}{2}$

$\text{λ}=\text{AB}\left(1+\text{cos 2}\text{α}\right)+\frac{\text{λ}}{2}$

$\frac{\text{λ}}{2}=\frac{\mathrm{h}}{\text{cos α}}\times 2{\text{cos}}^2\text{α}$

$\frac{\text{λ}}{2}=2\text{h cos α}$

$\mathrm{h}=\frac{\text{λ}}{\text{4 cos α}}$