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In the measurement of the angle of a pri...

In the measurement of the angle of a prism using a spectrometer, the readings of first reflected image are vernier I : `320^(@) 40'` , vernier II : `140^(@) 30'` and those of the second reflected image are vernier I : `80^(@) 38'` , vernier II : `260^(@)` 24'. Then, the angle of the prism is

A

`60^(@)58'`

B

`59^(@)58'`

C

`60^(@)2'`

D

`60^(@)4'`

Text Solution

Verified by Experts

Angle of the prism,
`A=(phi)/(2)`
Now, `phi=(phi_(1)+phi_(2))/(2)`
where, `phi_(1)=x_(2)-x_(1)`
`=(360^(@)+80^(@)38')-(320^(@)40')`
`=119^(@)=58'`
and `phi_(2)=y_(2)-y_(1)`
`=260^(@)24'-140^(@)30'=119^(@)54'`
`phi=(119^(@)58'+119^(@)54')/(2)=(239^(@)52')/(2)`
The angle to prism, `A=(phi)/(2)=(239^(@)52')/(4)=59^(@)58'`
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