A concave mirror has a radius of curvature of 34.0 cm. (b) If the mirror is immersed in water (refractive index 1.33), what is its focal length?

Verified step by step guidance

1. Identify the formula for the focal length of a mirror in air, which is given by \( f = \frac{R}{2} \), where \( R \) is the radius of curvature.
2. Calculate the focal length in air using the given radius of curvature, \( R = 34.0 \, \text{cm} \).
3. Understand that when the mirror is immersed in water, the focal length changes due to the refractive index of the medium. The new focal length \( f' \) can be calculated using the formula \( f' = \frac{f}{n} \), where \( n \) is the refractive index of the medium (water in this case).
4. Substitute the refractive index of water, \( n = 1.33 \), and the focal length in air calculated in step 2 into the formula from step 3.
5. Calculate the new focal length \( f' \) of the mirror when it is immersed in water.

Key Concepts

Focal Length of a Mirror

The focal length (f) of a concave mirror is related to its radius of curvature (R) by the formula f = R/2. This relationship indicates that the focal point, where parallel rays converge, is located at half the distance of the radius of curvature from the mirror's surface.

Refraction and Refractive Index

The refractive index (n) of a medium indicates how much light slows down when it enters that medium. In this case, the mirror is immersed in water, which affects the effective focal length due to the change in the speed of light, requiring adjustments in calculations to account for the medium's refractive properties.

Mirror Formula

The mirror formula relates the object distance (u), image distance (v), and focal length (f) of a mirror: 1/f = 1/v + 1/u. This formula is essential for understanding how the position of the object affects the image formed by the mirror, especially when considering changes in the surrounding medium.