The main scale of a spectrometer is divided such that one main scale division is equal to 0.5^ . A vernier scale is attached to it, in which 60 vernier scale divisions exactly coincide with 56 main scale divisions. The least count of the spectrometer, in arc minutes, is:

Step-by-step solution

Given, 1 MSD = 0.5^ . Since 1^ = 60' , we convert the main scale division into arc minutes: 1 MSD = 0.5 60' = 30' It is given that 60 vernier scale divisions (VSD) coincide with 56 main scale divisions (MSD). 60 VSD = 56 MSD 1 VSD = 56 60 MSD The least count (LC) of the spectrometer is defined as: LC = 1 MSD - 1 VSD LC = 1 MSD - 56 60 MSD = 4 60 MSD Substituting the value of 1 MSD in arc minutes: LC = 4 60 30' = 2' The least count is 2 arc minutes. Answer: 2