Question

the refractive index of a medium can be obtained by using the brewster's law given by u = tan (ib), where b is brewster angle. of ib is measured as ib = (45°+or-1°), then percentage error in u is p%. find value of 2p to nearest integer.


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Answer 1

Given info : The refractive index of a medium can be obtained by using the brewster's law given by $\mu=tan(i_B)$, where $i_B$  is brewster angle and of $i_B$ is measured as (45 ± 1)°.

To find : the percentage error in μ is p % then the value of 2p to nearest integer is ...

solution : $\mu=tan(i_B)$

differentiating both sides, we get

$d\mu=sec^2(i_B)d(i_B)$

⇒ $\Delta\mu=sec^2(i_B)\Delta i_B$

here, $i_B=45^{\circ}$ and $\Delta i_B=1^{\circ}$ = π/180 rad

$\mu=tan(i_B)$ = tan45° = 1

⇒ Δμ = sec²45° × π/180= (√2) × π/180 = π/90 rad

now the percentage error in μ = Δμ/μ × 100 = (π/90)/1 × 100 = 3.49 ≈ 3.5 %

as it has given that the percentage error in μ is p %

so the value of p = 3.5

the value of 2p = 2 × 3.5 = 7