Intensity obseverd in an interferecne pattern is `I = I_(0) sin^(2) theta`. At `theta = 30^(@)`, Intensity `I = 5 +- 0.002`. The pecentage error in angle is

Options

A. `4sqrt(3)xx10^(-2)%`
B. `(4)/(pi)xx10^(-2)%`
C. `(4sqrt(3))/(pi)xx10^(-2)%`
D. `sqrt(3)xx10^(-2)%`

Answer

C

Explanation

`I=I_(0) sin^(2) theta (dI)/(dtheta)=I_(0)xx2sin theta cos theta`
`(dI)/(I) = (I_(0)xx2sin theta cos theta d theta)/(I_(0)sin^(2)theta) = 2 cot theta d theta`
`%` error in angle
`(d theta)/(theta)xx100 = ((dI)/(I)xx(1)/(2cot theta))xx(1)/(theta)xx100`
`(d theta)/(theta)xx100=(0.002)/(2xx5 cot 30^(@))xx100xx(6)/(pi)`
`= (6)/(pi)xx(1)/(5)xx(1)/(sqrt(3))xx0.1=(6)/(pi)xx(1)/(5)xx(1)/(10)xx(1)/(sqrt(3))`
`= (sqrt(3))/(pi)xx(1)/(25) = (sqrt(3))/(pi)xx0.04 (d theta)/(theta)xx100 = (4 sqrt(3))/(pi)xx10^(-2)%`