A rod AB of length 5 cm is placed in front of a concave mirror of focal length 10 cm as shown in figure. The length of the image of AB formed by the mirror is

Explanation

See figure to understand the placement of object .

Point A is centre of curature of mirror and AB is rod since point A lies On centre of curvature of concave mirror , its image will be formed on itself . We have to find image of the point B. length of AB is f/8 hence
`PB = 2 f - f/8 = ( 16 f - f) /(8) = ( 15 f)/( 8 )`
PB will act as object distance in mirror formula
`1/f =1/v +1/u` ,br> ` implies (1)/(-f) = (1)/(v) + (1) /( -15 f //8)`
`implies 1/v = (-15 +8 )/( 15 f ) =- (7)/( 15 f)`
`implies v= - ( 15 F )/ (7) `
hence `PB. = 15 f//7 `
Length of the image
` AB. = PB. -PA `
` implies AB. = ( 15 f)/( 7) - 2f`
` implies Ab. = ( 15 f -14 f)/(7)`
`implies AB . (f)/(7)`