A cylindrical pin $$25_{ + 0.010}^{ + 0.020}\,\,mm$$ diameter is electroplated. Plating thickness is
$${2.0^{ \pm 0.005}}\,\,mm$$. Neglecting the gauge tolerance, the diameter (in $$mm,$$ up to $$3$$ decimal points accuracy) of the $$GO$$ ring gauge to inspect the plated pin is ___________

Assume that the surface roughness profile is triangular as shown schematically in the figure. If the peak to valley height is $$20$$ $$\mu m$$ The central line average surface roughness $${R_a}$$ (in $$\mu m$$) is

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