Question

The focal length of a concave mirror is

• A. Positive
• B. Negative
• C. both (A) and (B)
• D. None of these

Hint:

A simple rule to remember: For mirrors and lenses, convergent devices (concave mirror, convex lens) have a real focus and their focal length is taken as negative for mirrors and positive for lenses. Divergent devices (convex mirror, concave lens) have a virtual focus and their focal length is positive for mirrors and negative for lenses. An easier rule: Concave Mirror f < 0, Convex Mirror f > 0.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In optics, the New Cartesian Sign Convention is used to assign positive or negative signs to distances like object distance (u), image distance (v), and focal length (f).

Step 2: Detailed Explanation:
According to the sign convention:
\begin{enumerate} \item The pole (P) of the mirror is taken as the origin.
\item The principal axis is the x-axis.
\item Light is assumed to travel from left to right.
\item All distances are measured from the pole.
\item Distances measured in the same direction as the incident light are positive.
\item Distances measured in the direction opposite to the incident light are negative.
\end{enumerate} For a concave mirror, the principal focus (F) is located in front of the reflecting surface. To measure the focal length (the distance from P to F), one must travel from the pole to the left, which is opposite to the direction of the incident light.
Therefore, the focal length of a concave mirror is always taken as negative.

Step 3: Final Answer:
According to the standard sign convention, the focal length of a concave mirror is negative.