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 correspods 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:

Options

A. 59 degree
B. `58.59` degree
C. `58.77` degree
D. `58.65` degree

Answer

D

Explanation

Least count of vernier scale
LC = 1MSD - 1VSD
30VSD = 29 MSD
`1 VSD= (29)/(30)` MSD
So, `LC= 1MSD - (29)/(30)MSD = (1)/(30)` MSD
One division in main scale has a measure of 0.5 degrees
`1 MSD =(1)/(2)` degrees
`(1)/(30)MSD= (1)/(2)xx(1)/(30)` degrees
`=(1)/(60)` degrees
LC = 1 minute
So, `LC =(1)/(60)` degrees
Total reading = MSR + VSR `xx` LC
`=(58.5+9xx(1)/(60))` degrees
`=(58.65)` degree