$A$ thin transparent film with refractive index $1.4$ is held on a circular ring of radius $1.8 \ cm$. The fluid in the film evaporates such that transmission through the film at wavelength $560 \ nm$ goes to a minimum every $12 \ seconds$. Assuming that the film is flat on its two sides, the rate of evaporation is . . . . . . $\pi \times 10^{-13} \ m^3/s$.

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 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.

$A$ parallel beam of light of intensity $I_0$ is incident on a coated glass plate. If $25 \%$ of the incident light is reflected from the upper surface and $50 \%$ of the light that enters the glass is reflected from the lower surface of the glass plate, the ratio of maximum to minimum intensity in the interference region of the reflected light is

In a Fresnel's biprism experiment,fringes are obtained in the focal plane of an eyepiece at a distance of $1 \ m$ from the slit. $A$ convex lens is placed between the biprism and the eyepiece. The images of the slit are formed at two positions of the lens. The distances between the two images of the slit at these two positions are $4.05 \times 10^{-3} \ m$ and $2.9 \times 10^{-3} \ m$ respectively. Calculate the distance between the slits.

In a biprism experiment, the maximum intensity is $I_0$. If the path difference between the two interfering waves is $\frac{\lambda}{3}$, then the intensity at the point on the screen is [$\sin 30^{\circ} = \cos 60^{\circ} = 0.5, \sin 60^{\circ} = \cos 30^{\circ} = \sqrt{3}/2$].