The thickness of a plate having refractive index $\mu$ which will produce a change in optical path equal to half the wavelength $\lambda$ of the light passing through it is

On a rainy day,a small oil film on water shows brilliant colours. This is due to:

$A$ soap film with refractive index $\mu = 4/3$ is illuminated by white light incident at an angle of $60^\circ$. $A$ dark band corresponding to a wavelength of $5500 \, \mathring{A}$ is observed in the reflected light. Find the minimum thickness of the film in $\mathring{A}$.

$A$ thin oil film of refractive index $1.2$ floats on the surface of water $(\mu = \frac{4}{3})$. When light of wavelength $\lambda = 9.6 \times 10^{-7} \ m$ falls normally on the film from air,it appears dark when seen normally. What is the minimum change in its thickness for which it will appear bright in normally reflected light by the same light?

In a biprism experiment,if the $5^{\text{th}}$ bright band with wavelength $\lambda_1$ coincides with the $6^{\text{th}}$ dark band with wavelength $\lambda_2$,then the ratio $(\lambda_1 / \lambda_2)$ is:

Some currency notes (to avoid counterfeits) change their colour as you tilt them. This is due to