$A$ zone plate of focal length $60\,cm$ behaves as a convex lens. If the wavelength of incident light is $6000\,\mathring{A},$ then the radius of the first half-period zone will be:

Mention the colours which have the least and the most wavelength in visible light.

Which of the following phenomena support the wave theory of light?
$(1)$ Scattering
$(2)$ Interference
$(3)$ Diffraction
$(4)$ Velocity of light in a denser medium is less than the velocity of light in a rarer medium

The difference in the number of wavelengths, when yellow light propagates through air and vacuum columns of the same thickness, is one. Find the thickness of the air column. Given: Refractive index of air $\mu_a = 1.0003$, Wavelength of yellow light in vacuum $\lambda_0 = 6000 \text{ Å}$.

Statement $(S)$: Using Huygen's eye-piece,measurements can be taken but are not correct.
Reason $(R)$: The cross wires,scale,and final image are not magnified proportionately because the image of the object is magnified by two lenses,whereas the cross-wire scale is magnified by one lens only.
Identify the correct option from the following:

The radius of the central zone of a circular zone plate is $2.3\,mm$. The wavelength of the incident light is $5893\,\mathring{A}$. The source is at a distance of $6\,m$. What is the distance of the first image in meters?