Q. 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
A) $58.59\ Degree$
B) $58.77\ Degree$
C) $58.65\ Degree$
D) $59\ Degree$
Explanation
$30\ VSD = 29\ MSD$ $1\ VSD = \frac{29}{30}\ MSD$ Least count of vernier $= 1\ M.S.D.\ - 1\ V.S.D.$ $= 0.5{^\circ} - \frac{29}{30} \times 0.5{^\circ} = \frac{0.5{^\circ}}{30}$ Reading of vernier $=$ M.S. reading $+$ V.S. reading $\times$ $L.C.$ $= 58.5{^\circ} + 9 \times \frac{0.5{^\circ}}{30} = 58.65$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.