## Lenses Science Notes

Important Points :

→ Indicate the following terms related to spherical mirrors in figure 7.1 : pole, centre of curvature, radius of curvature, principal focus.

→ The given part of a hollow spherical glass can be converted into a concave mirror by

• polishing (silvering) its inner side (inner surface or concave surface) to make it reflecting or
• coating its outer side with a thin layer of silver and painting it with red colour to protect the silver coating.

[Note: Case (i) corresponds to the front surface silvered concave mirror.

→ The given part of a hollow spherical glass can be converted into a convex mirror by

• polishing (silvering) its outer side (outer surface or convex surface) to make it reflecting or
• coating its inner side with a thin layer of silver and painting it with red colour to protect the silver coating.

Note : Case (1) corresponds to the front surface silvered convex mirror

Lenses :

Lens : A lens is a transparent material bound by two surfaces, out of which at least one surface is spherical

→ Convex lens: A lens having both spherical surfaces puffed up outwards is called a convex lens or double convex lens or biconvex lens. A lens having one surface plane and the other (spherical surface) bulging outward is called a planoconvex lens.

→ A convex lens is thicker in the middle than at the edges. It is a converging lens. The concavo-convex lens has one spherical surface concave and the other convex such that it behaves as a convex lens.

→ Concave lens: A lens having both spherical surfaces curved inwards is called a concave lens or double concave lens or biconcave lens. A lens having one surface plane and the other (spherical surface) curved inwards is called a plano-concave lens.

→ A concave lens is thicker at the edges than in the middle. It is a diverging lens. The convexo-concave lens has one spherical surface convex and the other concave such that it behaves as a concave lens.

→ Centre of curvature (C) of a lens : The centres of the spheres whose parts form the surfaces of a lens are called the centres of curvature of the lens. A lens has two centres of curvature C, and C for its two spherical surfaces.

→ Radii of curvature (R, R) of a lens : The radii of the spheres whose parts form surfaces of a lens are called the radii of curvature of the
lens.

→ Principal axis of a lens : The imaginary straight line passing through the two centres of curvature of a lens is called the principal axis of the lens.

→ Optical centre (O) of a lens : The point inside a lens on the principal axis, through which light rays pass without changing their path is called the optical centre (O) of the lens.

→ Principal focus (F) of a lens : When light rays parallel to the principal axis are incident on a convex lens, they converge at a point on the principal axis. This point is called the principal focus (F) of the convex lens.

→ Light rays travelling parallel to the principal axis of a concave lens diverge after refraction in such a way that they appear to be coming out of a point on the principal axis. This point is called the principal focus of the concave lens. A lens has two principal foci F, and F.

→ Focal length of a lens : The distance between the optical centre and the principal focus of a lens is called the focal length of the lens.

Ray diagram for refracted light :

→ Rules for obtaining an image formed by a convex lens:

• When the incident ray is parallel to the principal axis, the refracted ray passes through the principal focus.
• When the incident ray passes through the principal focus, the refracted ray is parallel to the principal axis.
• When the incident ray passes through the optical centre of the lens, it passes without changing its direction.

[Note: Here, a ray means a ray of light.]

→ Image formation by a convex lens:

 Position of the object Position of the image Size of the image (relative to the size of the object) Nature of the image At infinity At focus F2 Point image Real and inverted Beyond 2FX Between F2 and 2F2 Smaller Real and inverted At 2FX                   ‘ At 2F2 Same size Real and inverted Between Fx and 2FX Beyond 2F2 Larger    _ Real and inverted At focus Fx At infinity Very large Real and inverted Between Fx and O On the same side of the lens as the object Very large Virtual and erect

[Note: In this chapter, no distinction is made between the terms focus and principal focus. Focus is also called focal point.]

→ An image formed by convergence of reflected or refracted rays of light at a point is called a real image.
An image formed at a point from which the reflected or refracted rays of light appear to diverge is called a virtual image.

→ A real image can be obtained on a screen. A virtual image cannot be obtained on a screen. Thus, if an image can be obtained on a screen, it must be real; if it cannot be obtained on a screen, it must be virtual. This is how we can find out whether an image is real or virtual.

→ Rules for obtaining an image formed by a concave lens:

• When the incident ray is parallel to the principal axis, the refracted ray, when extended backwards, passes through the principal focus.
• When the incident ray is directed towards the principal focus Fy, the refracted ray is parallel to the principal axis.
• When the incident ray passes through the optical centre of the lens, it passes without changing its direction.

→ The image formed by a concave lens is always virtual, erect and smaller than the object. It is on the same
side of the lens as the object. Generally, it is formed between the optical centre of the lens and the principal focus F1. If the object is at infinity, the image is a point image formed at F1.

 Position of the object Position of the image Size of the image (relative to the size of the object) Nature of the image At infinity On the first focus Fx Point image Virtual and erect Anywhere between optical centre O and infinity Between optical centre and focus Fx Small Virtual and erect

→ According to the Cartesian sign convention, the pole (P) of a spherical mirror is taken as the origin and the principal axis is taken as X-axis of the coordinate system.

• The object is always placed on the left of the mirror.
• All distances parallel to the principal axis are measured from the pole of the mirror.
• All distances measured to the right of the origin (pole) are taken as positive while distances measured to the left of the origin (pole) are taken as negative.
• Distances measured perpendicular to and above the principal axis are taken as positive.
• Distances measured perpendicular to and below the principal axis are taken as negative.
• The focal length of a convex mirror is positive while that of a concave mirror is negative.

Sign convention :

→ Sign convention for a lens : In this case, the optical centre (O) of the lens is taken as the origin and the principal axis of the lens is taken as X-axis of the coordinate system. The sign conventions regarding the measurement of distances parallel to the principal axis and those perpendicular to the principal axis are the same as for a spherical mirror. Hence, the focal length of a convex lens is positive and that of a concave lens is negative.

→ Lens formula: The relationship between the object distance (u), image distance (v) and focal length of a lens is called the lens formula and is given as $$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$$

→ Magnification by a lens : The magnification (M) produced by a lens
= $$\frac{\text { height of the image }\left(h_{2}\right)}{\text { height of the object }\left(h_{1}\right)}=\frac{v}{u}$$

Magnification is positive for a virtual image and negative for a real image.

→ Power of a lens : The power (P) of a lens
= $$\frac{1}{\text { focal length }(f) \text { of the lens }}$$
Its SI unit is the dioptre (D).
If f = 1 metre, P = 1 dioptre.

→ Combination of lenses : If two lenses with focal lengths f1 and f2 fare kept in contact with each other, the effective focal length of the combination, f, is given by $$\frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$$

→ The effective power of the combination of the lenses, P, is given by P = P1 + P2, where
p = $$\frac{1}{f}$$, P1 = $$\frac{1}{f_{1}}$$ and P2 = $$\frac{1}{f_{2}}$$

Working of the human eye and lens :

→ Power of accommodation of the eye : The ability of the eye lens to adjust its focal length is called the power of accommodation of the eye.

→ The minimum distance of distinct vision and the near point: The minimum distance from the normal eye at which an object is clearly visible without stress on the eye is called the minimum distance of distinct vision. It is 25 cm for the normal human eye.

→ The position of the object at the minimum distance of distinct vision is called the near point of the eye. For a normal human eye, the near point is at 25 cm from the eye.

→ The minimum distance of an object from a normal eye, at which it is clearly visible without stress on the eye, is called as minimum distance of distinct vision. The position of the object at this distance is called the near point of the eye, for a normal human eye, the near point is at 25 cm.

→ The farthest distance of an object from a human eye, at which it is clearly visible without stress on the eye is called farthest distance of distinct vision. The position of the object at this distance is called the far point of the eye For a normal human eye, the far point is at infinity.

→ The eye ball is approximately spherical and has a diameter of about 2.4 cm. The working of the lens in human eye is extremely important. The lens can change its focal length to adjust and see objects at different distances. In a relaxed state, the focal length of healthy eyes is 2 cm. The other focus of the eye is on the retina

Defects of vision and their correction :

→ Myopia or Nearsightedness : Myopia or near sightedness is the defect of vision in which a human eye can see nearby objects distinctly but is unable to see distant objects clearly. In this case, the image of a distant object is formed in front of the retina. This defect can be corrected using a concave lens of suitable focal length.

→ Hypermetropia or Farsightedness: Hypermetropia or farsightedness is the defect of vision in which a human eye can see distant objects distinctly but is unable to see nearby objects clearly. In this case, the image of a nearby object would fall behind the retina. This defect can be corrected using a convex lens of
suitable focal length.

→ Presbyopia (also called old age hyper metropia): Presbyopia is the defect of vision in which aged people find it difficult to see the nearby objects comfortably and clearly without spectacles. This defect can be corrected using a convex lens of suitable focal length.

Uses of lenses :

→ Uses of a convex lens : Simple microscope, compound microscope, telescope, camera, projector, spectrometer, spectacles, etc., make use of one or more convex lenses. A simple microscope is used by watch repairers, Jewellers, etc. A compound microscope is used to observe bacteria, cells, microorganisms, etc. A telescope is used to observe distant terrestrial objects or astronomical objects like planets, stars and comets.

→ Uses of a concave lens: A concave lens is used in spectacles to correct myopia. It is also used in optical instruments.

→ Persistence of vision: The image of an object remains imprinted on our retina for $$\frac{1}{16}$$th of a second after the object is removed from the sight. The sensation on the retina persists for a while. This is called persistence of vision. The retina in our eyes is made of many light sensitive cells. Due to these cells, we get information about the brightness or dimness of the object as well as the colour of the object