Question

A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: 58.5 degree, Vernier scale reading : 9 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. $58.59degree$
• B. $58.77degree$
• C. $58.65degree$
• D. $59degree$

Answer 1

The correct option is C $58.65degree$

$30VSD\to 29MSD$
$1VSD\to \frac{29}{30}MSD$

Least count of vernier $=1MSD-1VSD$
$={0.5}^0-\frac{29}{30}\times {0.5}^0$
$=\frac{{0.5}^0}{30}$

Reading of vernier $=$ M.S. reading + (V.S. reading $\times$ least count)
$={58.5}^0+(9\times \frac{{0.5}^0}{30})$
$={58.65}^0$