The circular main scale of a spectrometer is divided such that each degree is split into 3 equal parts. The Vernier scale attached to it has 60 divisions, which exactly coincide with 59 main scale divisions. The least count of the spectrometer in seconds of arc is:

Step-by-step solution

First, find the value of one main scale division (MSD). Since 1^ is divided into 3 equal parts, and 1^ = 60^ (minutes of arc): 1 MSD = 60^ 3 = 20^ Given the coincidence on the Vernier scale: 60 VSD = 59 MSD 1 VSD = 59 60 MSD The least count (L.C.) is: L.C. = 1 MSD - 1 VSD L.C. = 1 MSD - 59 60 MSD = 1 60 MSD Substitute the value of 1 MSD : L.C. = 1 60 20^ = 1 3 ^ Convert the least count into seconds of arc ( 1^ = 60^ ): L.C. = 1 3 60^ = 20^ Answer: 20