1.

For a concave mirror the magnificant of a real image was found to be twice as greater when the object was 15 cm from the mirror as it was when the object was 20 cm from the mirror. The focal length mirror isA. 5.0 cmB. 7.5 cmC. 10 cmD. 12.5 cm

Answer» Correct Answer - C
When object is at distance 15 cm, magnification is `2lamda` when object is at distance 20 cm, magnification is `lamda`
`m_1=-lamda,u_1=-20cm`
`m=-(v)/(u)implies-lamda=-(v_1)/(-20)`
`v_1=-20lamda`
`m_2=-2lamda,u_2=-15cm`
`m=-(v)/(u)implies-2lamda=-(v_2)/(-15)`
`v_2=-30lamda`
`(1)/(f)=(1)/(v_2)+(1)/(u_2)=(1)/(v_1)+(1)/(u_1)`
`(1)/(-30lamda)+(1)/(-15)=(1)/(-20lamda)+(1)/(-20)`
`(1)/(20lamda)-(1)/(30lamda)=-(1)/(20)+(1)/(15)`
`(1)/(60lamda)=(-3+4)/(60)implieslamda=1`
`(1)/(f)=(1)/(v_2)+(1)/(u_2)=(1)/(-30lamda)+(1)/(-15)`
`=(1)/(-30)+(1)/(-15)=(-(1+2))/(30)`
`f=-10cm`


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