For the given concave mirror, the focal length is f=−10 cm.
The rod lies along the principal axis. From the figure, the near end of the rod is at a distance of 20 cm from the pole of the mirror. Since the length of the rod is 10 cm, the far end is at a distance of 20+10=30 cm from the pole.
Let the near end be A and the far end be B.
Object distance for end A, uA=−20 cm.
Object distance for end B, uB=−30 cm.
Using the mirror formula, v1+u1=f1
For end A:
vA1+−201=−101
vA1=201−101=−201
vA=−20 cm
For end B:
vB1+−301=−101
vB1=301−101=301−3=−302=−151
vB=−15 cm
The length of the image is the distance between the images of the two ends:
Length of image=∣vA−vB∣=∣−20−(−15)∣=∣−5∣=5 cm.
Answer: 5
