Question

In a theodolite, the circular main scale is divided into degrees and each degree is divided into six parts. If the theodolite is to have a least count 20", then_________main scale divisions are divided into______vernier scale divisions.

• A. 29, 30
• B. 60, 59
• C. 59, 60
• D. 30, 29

Answer 1

The correct option is A 29, 30

We know that,

$Leastcount=\frac{s}{n}$

$Here,Leastcount,LC={20}^{\prime \prime }$

$s=\frac{1^o}{6}=\frac{(60\times 60{)}^{\prime \prime }}{6}[1^o={60}^{\prime }=(60\times 60{)}^{\prime \prime }]$

$\therefore 20=\frac{10\times 60}{n}$

$\Rightarrow n=30$

$\therefore \text{In case of theodolite, n divisions of vernier scale are equal to (n - 1) divisions of main scale}.$

$\therefore \text{(30) divisions of vernier scale are divided into (29) divisions of the main scale.}$