Question

Which of the following is the focal length of a convex mirror whose radius of curvature is 32 cm?

• A. -8 cm
• B. +8 cm
• C. -16 cm
• D. +16 cm

Hint:

Concave mirrors have positive focal length, convex mirrors have negative focal length as per sign convention.

Answer 1

The Correct Option is A

Step 1: Formula:
For spherical mirrors, the relationship between focal length ($f$) and radius of curvature ($R$) is: \[ f = \frac{R}{2} \] Step 2: Substitution:
Here, $R = 32 \, \text{cm}$, so: \[ f = \frac{32}{2} = 16 \, \text{cm} \] Step 3: Sign Convention:
For a convex mirror, the focal length is always taken as negative (because the focus lies behind the mirror). Thus: \[ f = -16 \, \text{cm} \]
Step 4: Final Answer:
The focal length of the convex mirror is -16 cm.