Physics, asked by Shubhamwalia, 1 year ago

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.

Answers

Answered by rohitkumargupta
25
\large{\mathbf{HELLO \: \: DEAR,}}

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

 \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}})<br />\\\\\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,<br />\: \: THANKS}}}
Answered by tiwaavi
9
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. :-)
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