Distance between virtual image, which is of twice of size of object placed in front of mirror and object is 45 cm. Magnitude of focal length of mirror is _______ cm.

$\left|m\right|=\left|\frac{v}{u}\right|=2$  

|v| = |2u|

n + 2n = 45

n = 15 cm

u = –15

v = 30

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

$\frac{1}{30}+\frac{1}{-15}=\frac{1}{f}$  

$\frac{1-2}{30}=\frac{-1}{30}=\frac{1}{f}$  

f = 30 cm

<div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1758870791php9FVWWS.jpeg" alt="" width="298" height="139" loading="lazy"></picture></div></div><p><span lang="EN-IN"><span contenteditable="false"> <math> <mrow> <mrow> <mo>|</mo> <mrow> <mi>m</mi> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mfrac> <mrow> <mi>v</mi> </mrow> <mrow> <mi>u</mi> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mn>2</mn> </mrow> </math> </span>&nbsp;</span></p><p><span lang="EN-IN">|v| = |2u|</span></p><p><span lang="EN-IN">n + 2n = 45</span></p><p><span lang="EN-IN">n = 15 cm</span></p><p><span lang="EN-IN">u = –15</span></p><p><span lang="EN-IN">v = 30</span></p><p><span lang="EN-IN"><span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mi>v</mi> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mi>u</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mi>f</mi> </mrow> </mfrac> </mrow> </math> </span>&nbsp;</span></p><p><span lang="EN-IN"><span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>3</mn> <mn>0</mn> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mo>−</mo> <mn>1</mn> <mn>5</mn> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mi>f</mi> </mrow> </mfrac> </mrow> </math> </span>&nbsp;</span></p><p><span lang="EN-IN"><span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mn>2</mn> </mrow> <mrow> <mn>3</mn> <mn>0</mn> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mn>3</mn> <mn>0</mn> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mi>f</mi> </mrow> </mfrac> </mrow> </math> </span>&nbsp;</span></p><p><span lang="EN-IN">f = 30 cm</span></p>

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