A concave mirror forms a real image of an object kept at a distance 9 cm from it. If the object is taken away from the mirror by 6 cm, the image size reduces to \frac{1}{4}^{th} of its previous size. Find the focal length of the mirror.

 

 

Answers (1)

m=\frac{f}{f-u}

case 1 u=-9 cm

m_1=\frac{f}{f+9}

case 2 u=-15cm

m_2=\frac{f}{f+15}

\\m_1=4m_2\\\frac{f}{f+9}=4\frac{f}{f+15}\\f+15=4f+36\\3f=-21\\f=-7cm

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