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A spectrometer gives the following readi...

A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading : `58.5 degree`
Vernier scale reading : `09` divisions
Given that `1` division on main scale correspods to `0.5` degree. Total divisions on the vernier scale is `30` and match with `29` divisions of the main scale. the angle of the prism from the above data:

A

`58.59^(@)`

B

`58.77^(@)`

C

`58.65^(@)`

D

`59^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
`1 "vernier scale division" =(29)/(60)` main scale division
`implies 1VSD=(29)/(30)xx0.5^(@)=((29)/(60))^(@)`
`:.` The least count `=1MSD-11VSD`
`=((1)/(2))^(@)-((29)/(60))^(@)=((1)/(60))^(@)`
so, reading `=` main scale reading`+`vernier scale reading
`=MSR+N X LC`
`=58.5^(@)+9xx((1)/(60))^(@)`
`=58.65^(@)`
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