Wave Optics Tes...

The question has a paragraph followed by two statements, Statement 1 and Statement 2. Of the given four alternatives after the statements, choose the one that best describes the statements.
A thin air film is formed by putting the convex surface of a plane convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.
Statement 1 : When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of $$\pi$$.
Statement 2 : The center of the interference pattern is dark.

The box of a pinhole camera of length L, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength $$\lambda $$ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size say $${b }_{ min }$$ when:

An initially parallel cylindrical beam travels in a medium of refractive index $$\mu(I) =\mu_0 + \mu_2 I$$, where $$\mu_0$$ and $$\mu_2$$ are positive constants and $$I$$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The initial shape of the wave front of the beam is 

To demonstrate the phenomenon of interference we require two soruces which emit radiation of

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency $$10\,GHz$$. What is the frequency of the microwave measured by the observer?
(speed of light $$=3\times 10^8 ms^{-1}$$)

In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is $$\cfrac { 1 }{ 8 } th$$ of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is:

In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit double of that from other slit. If $$\mathrm{I}_{\mathrm{m}}$$ be the maximum intensity. The resultant intensity $$I$$ when they interfere at phase difference $$\phi$$ is given by

A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale)

In a Young's double slit experiment, the slit separation d is $$0.3$$ mm and the screen distance D is $$1 m$$. A parallel beam of light of wavelength $$600 \, nm$$ is incident on the slits at angle $$\alpha$$ as shown in figure. On the screen, the point O is equidistant from the slits and distance PO is $$11.0 $$mm. Which of the following statement (s) is/are correct ?

The diameter of the objective lens of microscope makes an angle $$'\beta\ '$$ at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index 'n'. Then the resolving power of the microscope.