The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch (p) and included angle of the thread are 4 mm and 60°, respectively. The diameter of the best size wire is _________ mm (round off to 2 decimal places).

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 ________________________.