Physics - Geometrical Optics Question with Solution | TestHub

The concave mirror formula is

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$.... (i)

Since, for a given concave mirror, focal length$f$is fixed, we partially differentiate Eq. (i) to get

$-\frac{\delta v}{v^2}=-\frac{\delta u}{u^2}=0$or$\delta v=-{\left(\frac{v}{u}\right)}^2 \delta u$...... (ii)

Multiplying Equation. (i) by$u$, we get

$\frac{u}{v}+1=\frac{u}{f}$or$\frac{v}{u}=\frac{f}{u-f}$..... (iii)

Using Equation. (iii) in Equation. (ii), we get

$\delta v=-{\left(\frac{f}{u-f}\right)}^2\delta u$

Given$\delta u=b.$Therefore

$\delta v=-{\left(\frac{f}{u-f}\right)}^{2}b$

The negative sign shown that image is longitudinally inverted. The magnitude of the size of the image is

$\left|\delta v\right|=b{\left(\frac{f}{u-f}\right)}^2$