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Least count on vernier scale in vernier theodolite is ______
20'
20''
20┬░
1''
20''
The least count of a vernier theodolite is the smallest angular measurement that can be reliably read from its vernier scale. For a standard surveyor's theodolite, this value is 20 arc-seconds (20'').
The least count of a vernier theodolite is the smallest angular measurement that can be reliably read from its vernier scale. For a standard surveyor's theodolite, this value is 20 arc-seconds (20'').
LC=nSтАЛ тАФ The fundamental formula for calculating the least count of a vernier instrument.
The principle involves the graduation of a primary scale (main scale) and a secondary sliding scale (vernier). The least count is determined by the relationship LC=nSтАЛ, where S is the value of the smallest division on the main scale and n is the number of divisions on the vernier scale. By aligning the graduations, an observer can resolve fractional parts of the main scale division.
A theodolite is an precision instrument used for measuring horizontal and vertical angles in surveying.
The 'vernier' principle allows for higher precision than reading the main scale alone through interpolation.
Common least counts range from 1'' to 20'' depending on the instrument's accuracy grade (Transit vs. Micrometer theodolite).
20 seconds represents 360020тАЛ degrees.
Provides high angular precision for triangulation.
Allows reading of fractional divisions without complex optical attachments.
Susceptible to reading errors (parallax) by the observer.
Physical vernier scales can wear out, losing graduation alignment over time.
Topographical surveying
Geodetic control surveys
Alignment of civil engineering structures
The symbol '' denotes arc-seconds, where 1┬░ = 60' (minutes) and 1' = 60'' (seconds).
Option A (20') is an angular measurement in minutes, incorrect for vernier resolution.
Option C (20┬░) is too large and would be ineffective for surveying.
Option D (1'') is usually reserved for higher precision micrometer theodolites, not standard vernier types.
B is correct тАФ The least count of a standard vernier theodolite is 20 arc-seconds.
Always verify the instrument type; electronic total stations use digital sensors, while theodolites rely on mechanical verniers or optical micrometers for angular resolution.
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