A concave mirror with its optic axis vertical and mirror...

A concave mirror with its optic axis vertical and mirror facing upward is placed at the bottom of the water tank. The radius of curvature of mirror is $40 \mathrm{~cm}$ and refractive index for water $\mu=4 / 3$. The tank is $20 \mathrm{~cm}$ deep and if a bird is flying over the tank at a height $60 \mathrm{~cm}$ above the surface of water, the position of image of a bird is: (a) $3.75 \mathrm{~cm}$ (b) $4.23 \mathrm{~cm}$ (c) $5.2 \mathrm{~cm}$ (d) $3.2 \mathrm{~cm}$

A concave mirror with its optic axis vertical and mirror facing upward is placed at the bottom of the water tank. The radius of curvature of mirror is $40 \mathrm{~cm}$ and refractive index for water $\mu=4 / 3$. The tank is $20 \mathrm{~cm}$ deep and if a bird is flying over the tank at a height $60 \mathrm{~cm}$ above the surface of water, the position of image of a bird is:
(a) $3.75 \mathrm{~cm}$
(b) $4.23 \mathrm{~cm}$
(c) $5.2 \mathrm{~cm}$
(d) $3.2 \mathrm{~cm}$

Key Concepts

Mirror Equation

The mirror equation (1/u + 1/v = 1/f) relates the object distance (u), image distance (v), and the focal length (f) for mirrors. It is a central tool for analyzing image formation by mirrors, allowing one to determine where an image will form given a known object position and mirror curvature.

Focal Length of a Spherical Mirror

For a spherical mirror, especially a concave mirror, the focal length is half the radius of curvature (f = R/2). This relationship is very useful when describing how the mirror converges or diverges light, and it does not change with the medium in which the mirror is placed because reflection is independent of the refractive index.

Refraction and the Apparent Depth Concept

When light passes from one medium to another, such as from air into water, refraction causes a shift in the apparent position of objects. In the paraxial (small?angle) approximation, an object in air will appear (to an underwater observer) to be closer to the interface by a factor of n_air/n_medium. This ‘apparent depth’ concept is key in problems where an object is seen through a refracting surface before the light reaches another optical element.

Combination of Reflection and Refraction

In a compound optical system that involves both refraction (at a flat interface) and reflection (by a mirror), one must combine the effects of both. The effective object distance for the mirror is found by first determining the apparent position of the object due to refraction, and then applying the mirror equation. This composite treatment is crucial for correctly locating the image formed by the overall system.

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