Question
An object is placed cm in front of a concave mirror of focal length cm. Find the position, nature, and magnification of the image.
Solution — Step by Step
Following the standard Cartesian sign convention with the pole at origin and incident light from the left: object distance cm (object to the left), focal length cm (concave mirror, focus on the same side as the object).
Common denominator :
The negative magnification means the image is inverted; magnitude means the image is three times the object size.
Final Answer: Image is at cm in front of the mirror, real, inverted, and magnified times.
Why This Works
The mirror formula assumes the Cartesian sign convention: distances measured against the incident-light direction are negative. For a concave mirror with the object beyond the focus but inside (here , , so ), we expect a real, inverted, magnified image — which matches our answer.
The negative value confirms the image is on the same side as the object (in front of the mirror), so it’s a real image. A positive would have indicated a virtual image behind the mirror.
Alternative Method
Use the magnification formula directly, skipping the explicit calculation of . Useful when the question only asks for magnification.
Forgetting the sign on for a concave mirror is the #1 error. Many students plug and get , then conclude “virtual image” — completely wrong. Concave is negative; convex is positive. Drill this until it’s automatic.
JEE and NEET often ask the same problem but stop at a different step — sometimes “find ”, sometimes “find ”, sometimes “find if cm”. Solve the whole pipeline once; the numbers carry over.