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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 corresponds 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

`59` degree

B

`58.59` degree

C

`58.77` degree

D

`58.65` degree.

Text Solution

Verified by Experts

The correct Answer is:
D
`30 V.S.D = 29M.S.D.`
`1.V.S.D.=(29)/(30)M.S.D=(29)/(30)xx0.5^(@)`
Least count `=1M.S.D.-1V.S.D.`
`0.5^(@)-(29)/(30)xx0.5^(@)=(0.5^(@))/(30)`
`:.` Reading`=M.S.` reading`+` V.S. reading `xx`least count
`=58.5^(@)+9xx(0.5^(@))/(30)=58.65^(@).`
Hence correct choice is `(d)`.
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