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**(a) **An object is placed just outside the principal focus of concave mirror. Draw a ray diagram to show how the image is formed, and describe its size, position and nature.**(b)** If the object is moved further away from the mirror, what changes are there in the position and size of the image?**(c) **An object is 24 cm away from a concave mirror and its image is 16 cm from the mirror. Find the focal length and radius of curvature of the mirror, and the magnification of the image.

**(a) **Ray Diagram- to show how the image is formed when an object is placed just outside the principal focus of the concave mirror.

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The **size **of the image is **magnified**, the **position **of the image is **beyond the center of curvature $(C)$** of the mirror, and the nature of the image is **real and inverted.**

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**(b) **If the object is moved further away from the mirror, the image will move towards the mirror and its size will decrease gradually.

**(c) Given:**

Distance of object, $u$= $-$24 cm

Distance of image, $v$= $-$16 cm

**To find:** Focal length of the mirror $(f)$, radius of curvature of the mirror $(R)$, and the magnification of the image, $(m)$.

**Solution:**

From the mirror formula, we know that-

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Substituting the given values in the mirror formula we get-

$\frac{1}{f}=\frac{1}{(-24)}+\frac{1}{(-16)}$

$\frac{1}{f}=-\frac{1}{24}-\frac{1}{16}$

$\frac{1}{f}=\frac{-2-3}{48}$

$\frac{1}{f}=\frac{-5}{48}$

$f\times {(-5)}=48$

$f=-\frac{48}{5}$

$f=-9.6cm$

Thus, the focal length $f$ of the concave mirror is **9.6 cm.**

For radius of curvature $(R)$, we know that-

**$R=2f$,** where R = Radius of curvature, and f = Focal length

$R=2\times {(-9.6)}$

$R=2\times {(-9.6)}$

$R=-19.2cm$

Thus, the radius of curvature $(R)$ of the mirror is **19.2 cm.**

$m=-\frac{v}{u}$

Substituting the given values in the magnification formula we get-

$m=-\frac{(-16)}{-24}$

$m=\frac{(16)}{-24}$

$m=-0.66$

Thus, the magnification $(m)$, of the mirror is **0.66.**

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Hence, the image is** real, inverted, **and **small in size.**