Light of wavelength $6000 \, \mathring{A}$ is incident on a thin glass plate of refractive index $1.5$ such that the angle of refraction in the plate is $60^\circ$. Find the thickness of the plate so that it appears dark in reflection.

$A$ thin film of thickness $t$ and refractive index $1.33$ is coated on glass with a refractive index of $1.50$. What is the minimum thickness $t$ required for strong reflection when light of wavelength $600 \, nm$ is incident normally?.......$nm$

To ensure almost $100$ per cent transmittivity,photographic lenses are often coated with a thin layer of dielectric material. The refractive index of this material is intermediate between that of air and glass (which makes the optical element of the lens). $A$ typically used dielectric film is $MgF_2$ $(n = 1.38)$. What should the thickness of the film be so that at the center of the visible spectrum $5500 \, \mathring{A}$ there is maximum transmission?

Assertion: At the first glance,the top surface of the Morpho butterfly's wing appears a beautiful blue-green. If the wind moves the colour changes.
Reason: Different pigments in the wing reflect light at different angles.

Light is incident on a glass plate $(\mu = 1.5)$ at an angle of $60^o$. A dark fringe is observed corresponding to a wavelength of $6000 \, \mathring{A}$. If the thickness of the glass plate is $1.2 \times 10^{-3} \, mm$, find the order of the interference fringe.

Oil floating on water looks coloured due to interference of light. What should be the order of magnitude of the thickness of the oil layer in order that this effect may be observed? (in $m$)