Question

A real image of 3 cm size is formed at a distance of 23 cm in a concave mirror of focal length 13.8cm. at what distance is the object placed from the mirror?? Who find out the size of the object.

Answer 1

$\large{\mathbf{HELLO \: \: DEAR,}}$

$\mathbf{GIVEN \: \: THAT:-} \\ \\ \mathbf{Image \: \: Distance(v) = -23 cm. } \\ \mathbf{ Focal \: \: length(f) = -13.8 cm. }$

$\mathbf{\underline{Now,}}$

$\mathbf{Using \: \: the \: \: Mirror's \: \: Formula,}$

$\mathbf{\frac{1}{f} = \frac{1}{v} + \frac{1}{u}}\\\\ \mathbf{\frac{1}{-13.8}=\frac{1}{-23} + \frac{1}{u}}\\ \\ \mathbf{\frac{1}{u}=\frac{1}{23} - \frac{1}{13.8}}\\ \\ \mathbf{\frac{1}{u}=\frac{13.8-23}{317.4}}\\ \\ \mathbf{\frac{1}{u}=\frac{-9.2}{317.4}}\\ \\ \mathbf{u = \frac{317.4}{-9.2}}\\ \\ \mathbf{u = - 34.5CM}\\ \\ \mathbf{THE \: \: IMAGE \: \: IS \: \: FORMED \: \: AT \: \: THE \: DISTANCE \: \: OF \: \: 0.029 CM \: \: ON \: \: THE SIDE \: \: OF \: \: THE \: \: MIRROR}\\ \\ \mathbf{SIZE \: \: OF \: \: THE \: \: OBJECT = MAGNIFICATION = \frac{-v}{u}}\\ \\ \mathbf{m = -(\frac{-23}{-34.5}}) \\\\\mathbf{m = -0.667cm}$

$\mathbf{MAGNIFICATION = \: \: HEIGHT \: \: OF \: \: THE \: \: IMAGE/HEIGHT \: \: OF \: \: THE \: \: OBJECT}$

$\mathbf{0.667 = 3/H_O}$

$\mathbf{\therefore H_o = 4.5 cm}\\ \\ \mathbf{H_o = 4.5 CM}$

$\large{\mathbf{\underline{I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}}}$

Answer 2

Given conditions ⇒

Image Distance(v) = 23 cm. (negative)
Focal length(f) = 13.8 cm. (negative)

Now, 
Using the Mirror's Formula,

 $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ 
∴ $\frac{1}{-13.8} = \frac{1}{-23} + \frac{1}{u}$
⇒ 1/u = 1/23 - 1/13.8
⇒ u = -34.5 cm.

Hence, the image is formed at the distance of 34.5 cm on the side of the Mirror. 


Now, Let us find the size of the Object.

Magnification = -v/u
  = -(-23/-34.5)
  = -(0.67)
  = -0.67 

Also, 
 Magnification = Height of the Image/Height of the Object.

  0.67 = 3/H₀
∴ H₀ = 4.48 cm.

H₀ = 4.48 × 10⁻² m


Hence, the Height of the Object is 4.48 × 10⁻² m.


Hope it helps. :-)