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A student , who wanted to find the R.I. ...

A student , who wanted to find the R.I. of the material of a prism , found the following . Angle of the prism = `60^(@)`, Angle of minimum deviation = `40^(@)` , But while calculating the R.I. by mistake , he considered the refracting angle as `50^(@)` . what is teh error in the value of the R.I. of the material of the prism ?

A

`0.12`

B

`0.13`

C

`0.14`

D

`0.15`

Text Solution

Verified by Experts

The correct Answer is:
C
` n_(1) = ( sin ((60^(@) + 40^(@))/(2)))/( sin 30^(@)) = (sin 50^(@))/( sin 30^(@))`
`therefore n_(1) = 2 xx sin 50^(@) = 2 xx 0.766 = 1.532`
`n_(2)= ( sin ((50^(@) + 40^(@))/(2)))/( sin 25^(@)) = (sin 45^(@))/(sin 25^(@))`
`therefore n_(2) = (0.707)/(0.4226) = 1.673`
`therefore n_(2) - n_(1) = 1.673 - 1.532 = 0.141 = 0.14`
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