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:

Options

A. `58.59^@`
B. `58.77^@`
C. `58.65^@`
D. `59^@`

Answer

(c )

Explanation

Here, main scale reading, `x= 58.8^@`
Vernier scale reading n =09 division
V.C =1MSD - 1 VSD
`=1 MSD - (29)/(30) MSD = (1)/(30)MSD`
`=(1)/(30)xx0.5^@ = (1^@)/(60)`
:. Angle of prism = x + n (V.C.)
`=58.5^@ + (9^@)/(60) = 58.65^@`