Question

the focal lenght of a concave mirror is 30 cm . find the position of the object in front of the mirror so that the image is three times the size of the object​

Answer 1

Refer to the attached file.

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Answer 2

Answer:

• Image distance = 60 cm,

• Object distance = - 20 cm.

Explanation:

Given:

• Focal length (f) = - 30 cm
• Magnification (m) = ± 3

To Find:

• Object distance (u).

Now, firstly we will find image distance by magnification formula,

$\tt{\implies m = -\dfrac{v}{u}}$

$\tt{\implies 3 = -\dfrac{v}{u}}$

$\tt{\implies -v = 3u}$

$\tt{\implies v = -3u\;\;\;\;...........(1)}$

Now, by using mirror formula we will find object distance.

$\tt{\implies \dfrac{1}{f}=\dfrac{1}{v} +\dfrac{1}{u}}$

$\tt{\implies \dfrac{1}{-30}=\dfrac{1}{-3u}+\dfrac{1}{u}}$

$\tt{\implies -\dfrac{1}{30}=\dfrac{-1+3}{3u}}$

$\tt{\implies -\dfrac{1}{30}=\dfrac{2}{3u}}$

$\tt{\implies -3u=60}$

$\tt{\implies u=\dfrac{60}{-3}}$

$\tt{\implies u=-20\;cm}$

Now, put the value of 'u' in Eq (1) to find image distance (v).

$\tt{\implies v=-3u}$

$\tt{\implies v=-3(-20)}$

$\tt{\implies v = 60\;cm}$

Hence,

• Image distance = 60 cm,

• Object distance = - 20 cm.

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