The Human Eye

Explanation: The ability of the eye lens to adjust its focal length using ciliary muscles to focus on both near and distant objects is called the power of accommodation.

The retina acts as a light-sensitive screen at the back of the eye where the image is formed. It contains rods and cones that convert light into electrical signals.

This is also known as the Near Point of the eye. It is the minimum distance at which objects can be seen most distinctly without strain.

The ciliary muscles modify the curvature of the eye lens. Relaxing makes the lens thin (increases focal length), and contracting makes it thick (decreases focal length).

Given Power ($P$) = -5.5 D

Since $f$ is negative, it is a concave lens (Myopia correction).

Given Power ($P$) = +1.5 D

Since $f$ is positive, it is a convex lens (Hypermetropia correction).

Problem Analysis: A myopic person cannot see distant objects (at infinity). To correct this, the lens must take an object at infinity ($u = \infty$) and form a virtual image at the person’s far point ($v = -80$ cm).

Result: A Concave Lens of power -1.25 D is required.

Problem Analysis: The person wants to read an object placed at the normal near point ($u = -25$ cm), but their eye can only focus if the image is formed at their own near point ($v = -1$ m = -100 cm).

Result: A Convex Lens of power +3.0 D is required.

The ciliary muscles can contract to increase the curvature of the eye lens only up to a certain limit. If an object is placed closer than 25 cm, the lens cannot become thick enough to focus the image on the retina. This causes strain and blurred vision.

The image distance in the eye remains constant.

The image is always formed on the retina. To maintain this fixed image distance, the ciliary muscles change the focal length of the eye lens.

• Far object: Muscles relax, focal length increases.
• Near object: Muscles contract, focal length decreases.

Stars twinkle due to Atmospheric Refraction.

1. Starlight travels through different layers of the atmosphere with varying densities (temperatures).

2. These densities keep changing continuously due to wind.

3. This causes the path of light rays to fluctuate, making the apparent position of the star shake and the amount of light entering our eye flicker. This effect is seen as twinkling.

1. Distance: Planets are much closer to Earth than stars. They appear as extended sources of light (a collection of points) rather than point sources.

2. Averaging Effect: The atmospheric fluctuations cancel out. If light from one part of the planet is dimmed, light from another part brightens. The total amount of light entering the eye remains constant, so they do not twinkle.

This is due to the Scattering of Light.

1. At sunrise/sunset, sunlight travels a longer distance through the thick atmosphere to reach us.

2. Blue light (shorter wavelength) is scattered away by the particles in the atmosphere.

3. Red light (longer wavelength) scatters the least and reaches our eyes. Hence, the sun appears red.

The blue color of the sky is caused by the scattering of sunlight by air molecules. In space, there is no atmosphere. Without air particles, there is no scattering of light. Therefore, no light reaches the astronaut’s eyes from the surroundings, making the sky appear dark.