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.

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.

In a biprism experiment, a steady interference pattern is observed on the screen kept at a distance of $100 \text{ cm}$ using a light of wavelength $5000 \text{ Å}$. Without changing the distance between the virtual sources of the slit, the source of light is replaced by a source of wavelength $6400 \text{ Å}$. Now, to reduce the fringe width by $20\%$ of its initial value, the screen should be moved

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.

In a Fresnel biprism experiment,the two positions of the lens give separations between the virtual slits as $16 \; cm$ and $9 \; cm$ respectively. What is the actual distance of separation (in $cm$)?

When a mica sheet of thickness $7 \ \mu m$ and refractive index $\mu = 1.6$ is placed in the path of one of the interfering beams in a biprism experiment, the central fringe shifts to the position of the seventh bright fringe. The wavelength of the light used is $............ \ \mathring{A}$.