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 3x cm. The value of x is ______.
Answer: 32
Solution
The rod lies along the axis from 35cm to 45cm before the concave mirror of focal length 20cm. With the sign convention f=−20cm in v1+u1=f1, the far end at u=−45cm images at
v=u−ffu=−45+20(−20)(−45)=−36cm,
and the near end at u=−35cm images at
v=−35+20(−20)(−35)=−3140cm.
The image length is the separation of these two points,
−36+3140=332cm,
so x=32.
JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Integer answer
