Human Eye and Colourful World

When the ciliary muscles are relaxed, the eye lens becomes thin, the focal length increases, and distant objects are clearly visible. To see nearby objects clearly, the ciliary muscles contract making the eye lens thicker, decreasing its focal length. Hence, the human eye lens is able to adjust its focal length to view both distant and nearby objects clearly on the retina. This ability of the eye to focus on objects at different distances is called the power of accommodation.

The near point of the eye is the minimum distance of the object from the eye, which can be seen distinctly without strain. For a normal human eye, this distance is 25 cm. The far point of the eye is the maximum distance to which the eye can see the objects clearly. The far point of the normal human eye is infinity.

A student has difficulty in reading the blackboard while sitting in the last row. It shows that he is unable to see distant objects clearly. He is suffering from myopia. This defect can be corrected by using a concave lens.

(b) Human eye can change the focal length of the eye lens to see the objects situated at various distances from the eye. This is possible due to the power of accommodation of the eye lens.

(d) The human eye forms the image of an object at its retina.

(c) The least distance of distinct vision is the minimum distance of an object to see clear and distinct image. It is 25 cm for a young adult with normal visions.

The power P of a lens of focal length f is given by: P = 1/f (where f is in metres).

(i) Power of the lens for distant vision = −5.5 D
Focal length, f = 1/P = 1/(−5.5) = −0.181 m
The focal length of the lens for correcting distant vision is −0.181 m. This is a concave (diverging) lens.

(ii) Power of the lens for near vision = +1.5 D
Focal length, f = 1/P = 1/(+1.5) = +0.667 m
The focal length of the lens for correcting near vision is +0.667 m. This is a convex (converging) lens.

The person is suffering from myopia. A concave lens is used to correct this defect.

Object distance, u = −∞ (infinity)
Image distance, v = −80 cm = −0.80 m (the far point of the myopic eye)
Using the lens formula: 1/f = 1/v − 1/u
1/f = 1/(−0.80) − 1/(−∞) = −1.25 − 0 = −1.25
∴ f = −0.80 m
Power, P = 1/f = 1/(−0.80) = −1.25 D

A concave lens of power −1.25 D is required to correct the defect.

When sunlight enters the Earth's atmosphere, it undergoes scattering by the gas molecules in the atmosphere. The scattering of light by molecules is known as Tyndall effect. Since blue light has a shorter wavelength, it gets scattered much more than red light (which has a longer wavelength). This scattered blue light reaches our eyes from all directions across the sky. Therefore, the sky appears blue during the day. (If there were no atmosphere, the sky would appear dark/black as seen by astronauts in outer space.)

A person suffering from hypermetropia can see distant objects clearly but faces difficulty in seeing nearby objects clearly. The eye lens focuses the incoming divergent rays beyond the retina. This defect is corrected by using a convex lens.

The person must see an object kept at 25 cm (near point of normal eye) by forming its virtual image at his near point (1 m away).

Object distance, u = −25 cm
Image distance, v = −1 m = −100 cm
Using the lens formula: 1/f = 1/v − 1/u
1/f = 1/(−100) − 1/(−25)
1/f = −1/100 + 4/100 = 3/100
∴ f = 100/3 cm = 1/3 m ≈ 0.33 m
Power, P = 1/f = 1/(1/3) = +3.0 D

A convex lens of power +3.0 D is required to correct hypermetropia.

A normal eye is unable to clearly see the objects placed closer than 25 cm because the ciliary muscles of eyes are unable to contract beyond a certain limit. If the object is placed at a distance less than 25 cm from the eye, then the object appears blurred and produces strain in the eyes.

Since the size of eyes cannot increase or decrease, the image distance remains constant. When we increase the distance of an object from the eye, the image distance in the eye does not change. The increase in the object distance is compensated by the change in the focal length of the eye lens. The focal length of the eyes changes in such a way that the image is always formed at the retina of the eye.

Stars emit their own light and they twinkle due to the atmospheric refraction of light. Stars are very far away from the earth. Hence, they are considered as point sources of light. When the light coming from stars enters the earth’s atmosphere, it gets refracted at different levels because of the variation in the air density at different levels of the atmosphere. When the star light refracted by the atmosphere comes more towards us, it appears brighter than when it comes less towards us. Therefore, it appears as if the stars are twinkling at night.

Planets do not twinkle because they appear larger in size than the stars as they are relatively closer to earth. Planets can be considered as a collection of a large number of point-size sources of light. The different parts of these planets produce either brighter or dimmer effect in such a way that the average of brighter and dimmer effect is zero. Hence, the twinkling effects of the planets are nullified and they do not twinkle.

During sunrise, the light rays coming from the Sun have to travel a greater distance in the earth’s atmosphere before reaching our eyes. In this journey, the shorter wavelengths of lights are scattered out and only longer wavelengths are able to reach our eyes. Since blue colour has a shorter wavelength and red colour has a longer wavelength, the red colour is able to reach our eyes after the atmospheric scattering of light. Therefore, the Sun appears reddish early in the morning.

The sky appears dark instead of blue to an astronaut because there is no atmosphere in the outer space that can scatter the sunlight. As the sunlight is not scattered, no scattered light reach the eyes of the astronauts and the sky appears black to them.