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 ________________________.

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

The diameter of a recessed ring was measured by using two spherical balls of diameter $${d_2} = 60mm$$ and $${d_1} = 40mm$$ as shown in the figure.

The distance $${H_2} = 35.55\,\,mm$$ and $${H_1} = 20.55\,\,mm$$. The diameter ($$D,$$ in $$mm$$) of the ring gauge is __________________.