Two optically flat plates of glass are kept at a small angle $$\theta $$ as shown in the figure. Monochromatic light is incident vertically.

If the wavelength of light used to get a fringe spacing of $$1$$ $$mm$$ is $$450$$ $$nm,$$ the wavelength of light (in $$nm$$) to get a fringe spacing of $$1.5$$ $$mm$$ is ________________________.

For the situation shown in the figure below the expression for $$H$$ in terms of $$r, R$$ and $$D$$ is

In the assembly shown below, the part dimensions are:
$$\eqalign{ & {L_1} = {22.0^{ \pm 0.01}}\,\,mm, \cr & {L_2} = {L_3} = {10.0^{ \pm 0.005}}\,\,mm, \cr} $$
Assuming the normal distributions of part dimensions, the dimension $${L_4}$$ in $$mm$$ for assembly condition would be,

A $$GO-No$$ $$GO$$ plug gauge is to be designed for measuring a hole of nominal diameter $$25$$ $$mm$$ with a hole tolerance of $$ \pm 0.015\,\,mm.$$ Considering $$10\% $$ of work tolerance to be the gauge tolerance and no wear condition, the dimension (in $$mm$$) of the $$GO$$ plug gauge as per the unilateral tolerance system is