7. Lenses

Explanation:

1. Farsightedness (hypermetropia): The eye sees distant objects clearly but not nearby objects. The image of a nearby object forms behind the retina. It is corrected by a convex lens, which converges the rays before they reach the eye.
2. Presbyopia: With age, the ciliary muscles lose their ability to change the focal length of the eye lens, and the near point shifts farther away. When a person has both near and far defects, a bifocal lens is used: the upper part is concave (for distant vision) and the lower part is convex (for reading).
3. Nearsightedness (myopia): The eye sees nearby objects clearly but distant objects appear indistinct. The image of a distant object forms in front of the retina. It is corrected by a concave lens, which diverges the rays.

1. Centre of curvature (C): The centres of the spheres whose parts form the surfaces of the lens. A lens with two spherical surfaces has two centres of curvature, C₁ and C₂.
2. Radius of curvature (R): The radii R₁ and R₂ of the spheres whose parts form the surfaces of the lens.
3. Principal axis: The imaginary line passing through both centres of curvature.
4. Optical centre (O): The point inside the lens on the principal axis, through which light rays pass without changing their path.
5. Principal focus (F): Rays parallel to the principal axis, after refraction through a convex lens, meet at a point on the principal axis. This point is the principal focus. A lens has two principal foci, F₁ and F₂.
6. Focal length (f): The distance between the optical centre and the principal focus of the lens.

The object should be kept at 2F₁, i.e. at a distance equal to twice the focal length (2f) from the lens.

The ray BC parallel to the principal axis passes through F₂ after refraction. The ray BO through the optical centre goes straight. They meet at B′. So the image A′B′ is formed at 2F₂. It is real, inverted and of the same size as the object.

1. The parts of a watch are very small and cannot be seen clearly with the naked eye.
2. A simple microscope is a convex lens of small focal length. When a small object is kept between its focus and the lens, it forms a virtual, erect and magnified image.
3. So the watch repairer can see the tiny parts clearly in an enlarged form and repair them.

1. The retina has two types of light-sensitive cells: rod-like cells and cone-like (conical) cells.
2. Rod cells respond to the intensity of light, even faint light, but they do not give information about colour.
3. Conical cells respond to colour, but they work only in bright light, not in faint light.
4. Hence we can sense colours only in bright light.

1. The eye lens can change its focal length (power of accommodation), but only up to a limit.
2. For a normal eye, the minimum distance of distinct vision (near point) is 25 cm.
3. For an object closer than 25 cm, the eye lens cannot become rounded enough to reduce its focal length further. The image forms behind the retina.
4. So the object is not seen clearly, even though it subtends a bigger angle at the eye.

1. An astronomical (refracting) telescope has two convex lenses: the objective lens and the eyepiece. Their principal axes are along the same straight line, and they are fitted in a metallic tube so that the distance between them can be changed.
2. The objective has a large diameter and a large focal length, so it collects maximum light from the distant object.
3. Rays from a distant star or planet are nearly parallel. The objective refracts them and forms a real, inverted and small image at its focus.
4. This image acts as the object for the eyepiece. It lies at (or just inside) the focus of the eyepiece.
5. The eyepiece has a small size and small focal length. It refracts the rays again and forms a magnified final image, which the eye sees.
6. With the same objective and different eyepieces, different magnifications can be obtained.

Iris:

1. The iris is a dark, fleshy screen behind the cornea. It has a small hole of changing diameter at its centre, called the pupil.
2. The iris controls the size of the pupil and so controls the amount of light entering the eye.
3. In bright light, the pupil contracts; in dim light, it widens.

Muscles connected to the lens (ciliary muscles):

1. These muscles change the shape, and therefore the focal length, of the eye lens.
2. For distant objects, the muscles relax, the lens becomes flat and its focal length increases.
3. For nearby objects, the muscles contract, the lens becomes more rounded and its focal length decreases.
4. This power of accommodation lets us see objects clearly at different distances.

Given: P = +1.5 D. To find: f

Focal length = +0.67 m. The power and focal length are positive, so it is a convex lens. A convex lens is used to correct farsightedness.

Given: h₁ = 5 cm, u = −25 cm, f = +10 cm (converging lens). To find: v, h₂

The image is formed at 16.7 cm on the other side of the lens. Its size is 3.3 cm. v is positive and h₂ is negative, so the image is real and inverted (and smaller than the object).

The total power of the combination is 6.2 D.

Given: u = −60 cm. The image is virtual and on the same side as the object, so v = −20 cm. To find: f

The focal length is −30 cm. It is negative, so the lens is a diverging (concave) lens.

Suggested slides for the presentation:

1. Title: Binoculars — two telescopes side by side, one for each eye.
2. Construction: Each half has a convex objective lens (large, collects light), two prisms (fold the light path and make the image erect), and a convex eyepiece (magnifies). A central focusing wheel moves the eyepieces.
3. Working: The objective forms a real, inverted image. The prisms turn it upright using total internal reflection. The eyepiece magnifies this image.
4. Why prisms: They make the image erect and fold the long light path, so binoculars are short and easy to hold.
5. Meaning of “8 × 40”: magnification 8 times, objective diameter 40 mm.
6. Uses: bird watching, wildlife viewing, sports events, ships and navy, army, astronomy.
7. Advantage over a telescope: both eyes are used, which gives depth (3-D) and less strain.