A short straight object of length l lies alon | vedclass

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(C) The given situation is shown in the figure.Let $AB$ be the object and $A^{\prime}B^{\prime}$ be the image.Here, $AB = l$, $A^{\prime}B^{\prime} =

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$\left(\frac{F}{F-X}\right)^2$

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(C) The given situation is shown in the figure.Let $AB$ be the object and $A^{\prime}B^{\prime}$ be the image.Here, $AB = l$, $A^{\prime}B^{\prime} = l^{\prime}$, and the object distance $u = -X$.Using the mirror formula, $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$, where $f = -F$ for a concave mirror:$\frac{1}{-F} = \frac{1}{v} + \frac{1}{-X}$$\frac{1}{v} = \frac{1}{X} - \frac{1}{F} = \frac{F-X}{FX}$$v = \frac{FX}{F-X}$For a small object placed along the principal axis, the longitudinal magnification $M$ is given by:$M = \frac{l^{\prime}}{l} = -\frac{dv}{du} = -\frac{d}{du} \left( \frac{fu}{u-f} \right) = -\frac{f^2}{(u-f)^2}$Substituting $u = -X$ and $f = -F$:$M = -\frac{(-F)^2}{(-X - (-F))^2} = -\frac{F^2}{(F-X)^2}$The magnitude of the longitudinal magnification is:$\left| \frac{l^{\prime}}{l} \right| = \left( \frac{F}{F-X} \right)^2$

Similar Questions

You are asked to design a shaving mirror assuming that a person keeps it $10\,cm$ from his face and views the magnified image of the face at the closest comfortable distance of $25\,cm$. The radius of curvature of the mirror would then be.....$cm$.

$A$ concave mirror forms a real image three times larger than the object on a screen. The object and screen are moved until the image becomes twice the size of the object. If the shift of the object is $6 \ cm$,find the shift of the screen and the focal length of the mirror.

Assertion $(A):$ The relation among $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason $(R):$ The laws of reflection are strictly valid for plane surfaces but not for large spherical surfaces.

If the coordinates of the position of an object are $(-60 \, cm, 6 \, cm)$,then the coordinates of the image will be:

The minimum distance between the object and its real image for a concave mirror is

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