The circular main scale of a spectrometer is divided into half-degrees ( 0.5^ ). It is observed that 30 divisions of the vernier scale coincide exactly with 29 divisions of the main scale. The least count of the spectrometer, in minutes, is:

Step-by-step solution

The value of one main scale division is 1 MSD = 0.5^ . Given that 30 vernier scale divisions (VSD) coincide with 29 main scale divisions (MSD), we can write: 1 VSD = 29 30 MSD The least count (LC) of the instrument is given by: LC = 1 MSD - 1 VSD LC = 1 MSD - 29 30 MSD = 1 30 MSD Substitute the value of 1 MSD : LC = 1 30 0.5^ = ( 1 60 )^ Since 1^ = 60 minutes , we convert the least count into minutes: LC = 1 60 60 minutes = 1 minute Answer: 1