Two spherical mirrors, one convex and other concave, each of same radius of curvature R 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 as shown in figure. The radius of 3rd image (taking the first reflection at the concave mirror, then the successive reflection at the convex mirror and finally successive reflection at concave mirror again) of the circle is a/(40+x), then value of x is
Physics · Mixed Chapter
JEE Mains

Question

Two spherical mirrors, one convex and other concave, each of same radius of curvature R 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 as shown in figure. The radius of 3rd image (taking the first reflection at the concave mirror, then the successive reflection at the convex mirror and finally successive reflection at concave mirror again) of the circle is a/(40+x), then value of x is

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Each mirror has focal-length magnitude R/2. The circle on the convex mirror is 2R from the concave mirror. Step 2: First reflection (concave): u₁=2R, v₁=2R/3, so |m₁|=1/3. Step 3: Second reflection (convex): object distance from convex mirror is 2R−2R/3=4R/3. Its virtual image distance is 4R/11, giving |m₂|=3/11. Step 4: Third reflection (concave): its object distance is 2R+4R/11=26R/11; image distance is 26R/41 and |m₃|=11/41. Step 5: Total transverse magnification is (1/3)(3/11)(11/41…