Using screw gauge of pitch $0.1$ $cm$ and $50$ divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as 

A spectrometer gives the following reading when used to measure the angle of a prism. 

Main scale reading : $58.5$ degree

Vernier scale reading : $09$ divisions

Given that $1$ division on main scale corresponds to $0 .5$ degree. Total divisions on the Vernier scale is $30$ and match with $29$ divisions of the main scale. The angle of the prism from the above data ……. $degree$

A travelling microscope is used to determine the refractive index of a glass slab. If $40$ divisions are there in $1 \; cm$ on main scale and $50$ Vernier scale divisions are equal to $49$ main scale divisions, then least count of the travelling microscope is $\dots \; \times 10^{-6} \; m$

One main scale division of a vernier callipers is $a$ $cm$ and $n ^{\text {th }}$ division of the vernier scale coincide with $( n -1)^{\text {th }}$ division of the main scale. The least count of the callipers in $mm$ is