Q Two spherical mirrors - one convex and the other concave, are each of the same radius r - Physics - Ray Optics And Optical Instruments

Question

Q Two spherical mirrors - one convex and the other concave, are
each of the same radius r They are arranged coaxially at a distance
2r from each other A small circle of radius a is drawn on the
convex mirror near the pole Prove that the radii of the first two
images are a/3 and a/ 11

Shobhit Mittal · Accepted Answer

for first image u=-2r,f=-r21v+1u=1f1v+1-2r=2-r1v=12r-2rv=-2r3m=-vu=-2r3-2r=13radius of first image a'a'a=13a'=a3for second image u=-2r-2r3=-4r3,v=r21v+1u=1f1v+1-4r3=1r21v=2r+34r=114rv=4r11m'=-vu=-4r11-4r3=311let the raddi of the second image be a''m'=a''a'311=a''a/3a''=a11Regards

Q. Two spherical mirrors - one convex and the other concave, are each of the same radius r. They are arranged coaxially at a distance 2r from each other. A small circle of radius a is drawn on the convex mirror near the pole. Prove that the radii of the first two images are a/3 and a/ 11.