Question

A spherical mirror is immersed in water. Its focal length will

• A. decrease
• B. increase
• C. remain same
• D. none of these

Hint:

A common point of confusion is between mirrors and lenses. Remember: \textbf{Mirror} → Reflection → Focal length depends on geometry (\(R/2\)) → \textbf{Unaffected} by medium. \textbf{Lens} → Refraction → Focal length depends on refractive indices → \textbf{Affected} by medium.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The focal length of a spherical mirror is determined by the laws of reflection and the geometry of the mirror's surface.
Step 2: Key Formula or Approach:
The focal length (\(f\)) of a spherical mirror is related to its radius of curvature (\(R\)) by the formula:
\[ f = \frac{R}{2} \] Step 3: Detailed Explanation:
The laws of reflection state that the angle of incidence is equal to the angle of reflection, and these angles are measured with respect to the normal at the point of incidence. These laws are independent of the medium in which the reflection occurs.
The formula \(f = R/2\) shows that the focal length of a mirror depends only on its radius of curvature (\(R\)), which is a physical property of the mirror's shape.
Unlike a lens, whose focal length depends on the refractive index of its material and the surrounding medium (as described by the Lens Maker's Formula), a mirror's focal length is purely a geometric property.
Therefore, immersing a spherical mirror in water (or any other transparent medium) does not change its radius of curvature, and consequently, its focal length remains the same.
Step 4: Final Answer:
Since the focal length of a spherical mirror depends only on its radius of curvature and not on the surrounding medium, it will remain the same when immersed in water. Option (C) is correct.