A thin cylindrical rod of length 10 cm is placed horizontally on the principle axis of a concave mirror of focal length 20 cm . The rod is placed in a such a way that mid point of the rod is at 40 cm from the pole of mirror. The length of the image formed by the mirror will be x 3 cm . The value of x is ______.

Step-by-step solution

As per sign conventions, object distance u A = - 45   cm , focal length f = - 20   cm . From the mirror formula 1 v A + 1 u A = 1 f ⇒ 1 v A + 1 - 45 = 1 - 20 ⇒ v A = - 45 × ( - 20 ) - 45 - ( - 20 ) = - 900 25 ⇒ v A = - 36   cm And u B = - 35   cm 1 v B + 1 u B = 1 f ⇒ 1 v B + 1 - 35 = 1 - 20 ⇒ v B = - 35 × ( - 20 ) - 35 - ( - 20 ) = 700 - 15 ⇒ v B = - 140 3   cm Now, length of image = v A - v B = - 36 + 140 3   cm = - 108 + 140 3   cm