The focal length of a mirror is given by frac | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the equation: $\frac{2}{f} = \frac{1}{v} - \frac{1}{u}$ $(i)$Taking the differential of both sides:$-\frac{2}{f^2} df = -\frac{1}{v^2} dv +

Vedclass · Accepted Answer

$p\left(\frac{1}{u} + \frac{1}{v}\right)$

Vedclass · Answer

(B) Given the equation: $\frac{2}{f} = \frac{1}{v} - \frac{1}{u}$ $(i)$Taking the differential of both sides:$-\frac{2}{f^2} df = -\frac{1}{v^2} dv + \frac{1}{u^2} du$Given that the errors in $u$ and $v$ are $p$,we have $dv = p$ and $du = p$.Substituting these into the differential equation:$-\frac{2}{f^2} df = -\frac{1}{v^2} p + \frac{1}{u^2} p$$-\frac{2}{f^2} df = p \left( \frac{1}{u^2} - \frac{1}{v^2} \right)$Using the identity $a^2 - b^2 = (a - b)(a + b)$:$-\frac{2}{f^2} df = p \left( \frac{1}{u} - \frac{1}{v} \right) \left( \frac{1}{u} + \frac{1}{v} \right)$From equation $(i)$,$\frac{1}{u} - \frac{1}{v} = -\frac{2}{f}$. Substituting this:$-\frac{2}{f^2} df = p \left( -\frac{2}{f} \right) \left( \frac{1}{u} + \frac{1}{v} \right)$Dividing both sides by $-\frac{2}{f}$:$\frac{df}{f} = p \left( \frac{1}{u} + \frac{1}{v} \right)$Thus,the relative error in $f$ is $p \left( \frac{1}{u} + \frac{1}{v} \right)$.

The focal length of a mirror is given by $\frac{2}{f} = \frac{1}{v} - \frac{1}{u}$. In finding the values of $u$ and $v$,the errors are equal to $p$. Then,the relative error in $f$ is

Similar Questions

The temperature of the hot junction of a thermocouple changes from $80\,^{\circ}C$ to $100\,^{\circ}C$. The percentage change in thermoelectric power is ............... $\%$.

The angle between the pair of straight lines formed by joining the points of intersection of $x^2+y^2=4$ and $y=3x+c$ to the origin is a right angle. Then $c^2$ is equal to

Which one of the following represents the correct order of electronegativity?

$A$ thin prism $P_1$ with angle $4^o$ and made from glass of refractive index $1.54$ is combined with another thin prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_2$ is (in $^o$)

The position vector of a point lying on the line joining the points whose position vectors are $\hat{i}+\hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+\hat{k}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module