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(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.

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

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(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.

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For distant vision $=-0.181 m$, for near vision $=0.667 m$

The power $P$ of a lens of focal length $f$ is given by the relation

$ P=\dfrac{1}{f(\text{ in metres })} $

(i) Power of the lens used for correcting distant vision $=-5.5 D$

Focal length of the required lens, $f=\dfrac{1}{P}$ $f=\dfrac{1}{-5.5}=-0.181 m$

The focal length of the lens for correcting distant vision is $-0.181 m$.

(ii) Power of the lens used for correcting near vision $=+1.5 D$

Focal length of the required lens, $f=\dfrac{1}{P}$

$f=\dfrac{1}{1.5}=+0.667 m$

The focal length of the lens for correcting near vision is $0.667 m$.

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The person is suffering from an eye defect called myopia. In this defect, the image is formed in front of the retina. Hence, a concave lens is used to correct this defect of vision.

Object distance, $u=$ infinity $=\infty$

Image distance, $v=-80 cm$

Focal length $=f$

According to the lens formula,

$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$

$-\dfrac{1}{80}-\dfrac{1}{\infty}=\dfrac{1}{f}$

$\dfrac{1}{f}=-\dfrac{1}{80}$

$f=-80 cm=-0.8 m$

We know,

Power, $P=\dfrac{1}{f(\text{ in metres })}$

$P=\dfrac{1}{-0.8}=-1.25 D$

A concave lens of power $-1.25 D$ is required by the person to correct his defect.

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A person suffering from hypermetropia can see distinct objects clearly but faces difficulty in seeing nearby objects clearly. It happens because the eye lens focuses the incoming divergent rays beyond the retina. This defect of vision is corrected by using a convex lens. A convex lens of suitable power converges the incoming light in such a way that the image is formed on the retina, as shown in the following figure.

Correction for hypermetropic eye

The convex lens actually creates a virtual image of a nearby object ( $N^{\prime}$ in the figure) at the near point of vision $(N)$ of the person suffering from hypermetropia.

The given person will be able to clearly see the object kept at $25 cm$ (near point of the normal eye), if the image of the object is formed at his near point, which is given as $1 m$.

Object distance, $u=-25 cm$

Image distance, $v=-1 m=-100 m$

Focal length, $f$

Using the lens formula,

$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$

$\dfrac{1}{-100}-\dfrac{1}{-25}=\dfrac{1}{f}$

$\dfrac{1}{f}=\dfrac{1}{25}-\dfrac{1}{100}$

$\dfrac{1}{f}=\dfrac{4-1}{100}$

$f=\dfrac{100}{3}=33.3 cm=0.33 m$

Power, $P=\dfrac{1}{f(\text{ in metres })}=\dfrac{1}{0.33 m}=+3.0 D$

A convex lens of power $+3.0 D$ is required to correct the defect.

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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.

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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.

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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.

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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.

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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.