A thin rod of length f/3 is placed also the optic axis of a concave mirror of focal length f such that its image which is magnified, just touches the rod. The magnitude of magnification of the rod is N/2. Find N.
Physics · Mixed Chapter
JEE Mains

Question

A thin rod of length f/3 is placed also the optic axis of a concave mirror of focal length f such that its image which is magnified, just touches the rod. The magnitude of magnification of the rod is N/2. Find N.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Let the rod length be L=f/3. For a concave mirror, a point at axial object distance u (>f) forms a real image at v=fu/(u−f). Step 2: As the magnified rod image just touches the rod, their adjacent ends coincide at the centre of curvature, 2f. Thus the rod extends from 5f/3 to 2f. Step 3: The object end at u=2f has image at v=2f. The other end at u=5f/3 has image v=(f·5f/3)/(2f/3)=5f/2. Step 4: Image length = 5f/2−2f=f/2. Longitudinal magnification = (f/2)/(f/3)=3/2=N/2. Hence N=3. Answe…