The thickness of a plate having refractive index $\mu$ which will produce a change in optical path equal to half the wavelength $\lambda$ of the light passing through it is

Which of the following produces coherent waves?

If a biprism experiment is immersed in water,and the fringe width in air is $\beta_a$,find the new fringe width if the refractive index of the biprism material is $1.5$ and the refractive index of water is $1.33$.

$A$ thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate with the curved surface downwards. Monochromatic light is incident normally from the top. The observed interference fringes from this combination do not follow one of the following statements.

$A$ thin oil film of refractive index $1.2$ floats on the surface of water $(\mu = \frac{4}{3})$. When light of wavelength $\lambda = 9.6 \times 10^{-7} \ m$ falls normally on the film from air,it appears dark when seen normally. What is the minimum change in its thickness for which it will appear bright in normally reflected light by the same light?

In a Fresnel's biprism experiment,a mica sheet of refractive index $1.5$ and thickness $6 \times 10^{-6} \ m$ is placed in the path of one of the interfering beams. As a result,the central fringe shifts by a distance equal to $5$ fringe widths. Find the wavelength of light in $\mathring{A}$.