A concave mirror of focal length 20 cm is cut into two equal pieces. Their poles are shifted to y=+2 cm and y=−2 cm without rotation, with parallel axes. A point object is on the original axis 30 cm away. Using first-order transverse imaging, find the separation between the two image y-coordinates in centimetres.
Physics · Geometrical optics · spherical mirror
JEE Mains NEET

Question

A concave mirror of focal length 20 cm is cut into two equal pieces. Their poles are shifted to y=+2 cm and y=−2 cm without rotation, with parallel axes. A point object is on the original axis 30 cm away. Using first-order transverse imaging, find the separation between the two image y-coordinates in centimetres.

Physics · Geometrical optics · spherical mirror

G1 Physics · Accepted Answer

For each shifted piece, object height relative to its own axis is ∓2 cm. At u=30 and f=20, m=−2. Image height relative to each piece axis is ±4 cm. Thus upper-piece image y=+2+4=+6; lower-piece image y=−2−4=−6. Separation=12 cm.