Question

The main scale of a spectrometer is divided into 720 division in all. If circular vernier scale consists of 30 divisions, the least count of the instrument is ______.

(Given: 30 vernier divisions coincide with 29 main scale divisions)

Options

• 0.1°

• 1''

• 1'

• 0.1''

Answer 1

The main scale of a spectrometer is divided into 720 division in all. If circular vernier scale consists of 30 divisions, the least count of the instrument is 1'.

Explanation:

Given, Total number of main scale division in spectrometer = 720

Total angle in main scale = 360°

Total angle required for the 720 main scale division = 360°

So, angle required for 1 main scale division

`(360°)/720=(1°)/2`

But, we know that 1° = 60 '

So, angle required for 1 main scale division

= `(60')/2` = 30'

As per the condition, 30 Vernier Scale Division (VSD) = 29 Main Scale Division (MSD)

1 VSD = `29/30` MSD

Least Count (LC) = 1MSD – 1VSD

LC = 1 - `29/30=1/30`

So, total angle in one least count

= `1/30` × 30' = 1'

Hence, the least count will be 1'.