Comprehensive WBBSE Class 10 Physical Science Notes Chapter 5 Light can help students make connections between concepts.
Light Class 10 WBBSE Notes
Reflection of light: Light travelling in one medium when falls on a second medium, a portion of the incident light, depending on the nature of the surface of the second medium, is turned back into the first medium. This phenomenon is known as reflection of light.
Laws of reflection:
- The incident ray, the reflected ray and the normal at the point of incidence on the reflecting surface line in one plane.
- The angle of incidence is equal to the angle of reflection.
Real Image and Virtual image: If rays diverging from a point source after reflection or refraction suffer changes or direction and either actually converge to, or appear to diverge from a second point, the second point is called the image of the first point and the image is real in the first case and virtual in the second case.
Characteristics of the image formed by plane mirror
- the image is virtual
- the image is erect
- the size of the image is equal to the size of the object
- the image is formed as for behind the mirror as the object is infront of it
- the image is laterally inverted.
Effect of rotation of a plane mirror on the reflected ray: For a given incident ray, if a mirror be rotated through angle say θ, the reflected ray rotates through double the angle (2θ).
Multiple images formed by two mirrors inclined at an angle: When an object is kept between two mirrors inclined at an angle θ, a number of images are formed due to multiple reflections.
The number of images formed = \(\left(\frac{2 \pi}{\theta}-1\right)\)
when θ = 90°, images formed 3.
when θ = 0°, images formed infinite.
Spherical mirrors: A spherical mirror is a reflecting surface so curved that it forms a part of a regular hollow sphere.
Centre of Curvature: The centre of the sphere of which the mirror is a part is called the centre of curvature of the mirror. C and C’ are the centres of curvatures of a concave and a convex mirror respectively.
Radius of curvature: The radius of the sphere of which the mirror is a part called its radius of curvature (r).
Aperture: The perimeter of a spherical mirror is generally circular in shape and diameter (AB) of this circle is called aperture of the mirror.
Pole: The central point (P) of the mirror is called its pole.
Principal axis: The straight line (XX’) passing through the pole and centre of curvature is called principal axis of the mirror.
Principal section: When a spherical mirror is intersected by a plane passing through the principal axis, the section is a circular arc (APB) called principal section of the mirror.
Principal focus: A beam of rays parallel to the principal axis of a spherical mirror after reflection either converges to (in case of a concave mirror) or appears to diverge from (in the case of a convex mirror) a fixed point (F) on the axis, which is called the Principal focus of the mirror.
Focal length: The distance of the focus from the pole of the mirror is called the focal length (PF) of the mirror.
Focal plane: The plane passing through the principal focus of a mirror and at right angle to its principal axis is called the focal plane of the mirror.
Sign conventions:
As the radius of curvature and focal length of a concave mirror are measured towards the left of its pole, so they are taken as negative in the new cartesian sign convention.
As the radius of curvature and focal length of a convex mirror are measured towards the right of its pole, so they are taken as positive in this sign convention.
Relation between radius of curvature and focal length
r = 2f
The mirror formula: The general equation for a spherical mirror is
\(\frac{1}{u}+\frac{1}{v}=\frac{2}{r}=\frac{1}{f}\)Linear magnification: The ratio of the linear size of the image to the linear size of the object is called the linear magnification.
m = \(\frac{h2}{h1}\) = \(\frac{-v}{u}\)
This relation is valid for both the mirrors (concave and convex).
In the case of a concave mirror depending on the position of the object, the image may be real, inverted, magnified, of same size or diminished and also virtual erect and magnified.
In the case of a convex mirror the image is always virtual, erect and diminished for all positions of the object.
The relation between the speed of object and fmage formed by a spherical mirror:
vi = speed of image
vo = speed of object
Applications of spherical mirrors:
- A concave mirror is used as a shaving mirror as it produces magnified erect image.
- A concave mirror is used as a reflector in search lights, head lights in cars, solar cookers etc.
- A concave mirror is used by the opticians in opthalmoscopes for reflecting light on the retina.
- A convex mirror is used as rear view mirrors, in automobiles as it always produces an erect image of diminished size giving a wide field of view.
- A convex mirror is used as a reflector in street lamps, as it can diverge light over a large area.
Refraction of light: The phenomenon of change in the direction of light ray, when it passes obliquely from one homogeneous medium to another is called refraction of light.
Laws of refraction:
The incident ray, the refracted ray and the normal at the point of incidence on the refracting surface lie in the same plane.
Snell’s Law: For a given pair of media and for a given colour of light, the sine of the angle of incidence bears a constant ratio to the sine of angle of refraction.
\(\frac{\sin t}{\sin r}\) = const = μ2 (refractive index)
Types of refractive index :
Absolute refractive index: The refractive index of a medium with respect to vacuum or air is taken as the absolute refractive index of the medium.
Relative refractive index: The refractive index of a medium with respect to any other medium is called its relative refractive index.
Principle of Reversibility of Light: The principle states that if the path of ray of light is reversed after so suffering a number of reflections and refractions, it retraces its path. Thus according to this principle, image and object positions can be interchanged. The points corresponding to object and image are called conjugate points.
Generalised Snell’s law of refraction:
μ1 sin i = μ2 sin r
Optically denser media: When the absolute refractive index of a medium is greater then that of a second medium, then the first medium is called the optically denser media than the second one.
Optically rarer media: The second medium is called optically rarer media.
Real depth and Apparent depth:
When μ1>μ2, real depth > apparent depth i.e. when the observer is in rarer medium the image appears closer to the surface than the object.
When μ2 = 1 i.e. when the observer in the air medium, μ1= μ = refractive index of the medium in which object is situated then
μ = \(\frac{\text { real depth }}{\text { apparent depth }}\)
When μ2>μ1 i.e. when the observer in the denser medium, the image appears further away from the surface than the object.
For this reason a tank filled with water or any transparent liquid appears less deep. Also a straight stick put obliquely in water appears bent. lens is called double convex lens. It is used in camera, telescope etc.
Refraction through a parallel slab:
\({ }_1 \mu_2 \times{ }_2 \mu_1=1\)Refraction through a compound slab:
\({ }_1 \mu_2 \times{ }_2 \mu_3={ }_1 \mu_3\)
Total internal reflection : It is a phenomenon in which a ray of light travelling from an optically denser medium to an optically rarer medium is incident at an angle greater than the critical angle for the pair of media in contact, the ray is totally reflected back into denser medium.
Conditions for total internal reflection :
- light must travel from a denser to a rerer medium.
- angle of incidence in the denser medium must be greater than the critical angle for the pair of media in contact.
Relation between refractive index and critical angle :
sin ic = \(\frac{1}{μ}\)
Spherical refracting surface: A refracting surface, which is a part of a sphere of transparent refracting material is known as a spherical refracting surface.
Types of spherical refracting surfaces :
- convex spherical refracting surface: These surface have convex towards rarer medium side.
- Concave spherical refracting surface: These surfaces have towards rarer medium side.
Refraction from rarer to denser medium at a convex spherical refracting surface:
Image formation by a concave mirror:
| Position of the object | Position of the image | Size of the image | Nature of the image |
| between | Behind the | Enlarged | virtual and erect |
| P and F | mirror | Highly enlarged | Real and inverted |
| A + F | A + infinity | Enlarged | Real and inverted |
| Between | Beyond C | Same size | Real and inverted |
| C and F | A + C | Diminished | Real and inverted |
| A + C | Between F and C | Highly dminished point sized | Real and inverted |
| Beyond C | At the focus F | Size of the image | Nature of the image |
| A + infinity | Position of the image | Enlarged | virtual and erect |
Image formation by a convex mirror:
| Position of the object | Position of the image | Size of the image | Nature of the image |
| At infinity | At the focus F, behind the mirror | Highly diminished point | virtual and erect |
| Between infinity and the pole P of the | Between P and F behind the mirror | sized | virtual and erect |
The new cartesian sign convention for spherical mirrors :
Absolute Refractive index of some material media:
Lenses: A lens is a portion of a transparent medium bounded by two polished surfaces with at least one of them being curved.
Types of Lenses: Lenses are broadly of two types :
- Convex lens: If the lens is thicker at its centre than at its edges, it is a convex lens.
- Concave lens: The lens which is thinner of the centre and wider at the two edges is called a concave lens.
Other types of lenses:
Double convex lens : If both the surfaces of convex lens are convex then the lens is called double convex lens. It is used in camera, telescope etc.
Plano-convex lens: If one surface of convex lens is plane and the other is cinvex then it is called plano convex lens. It is used in eye piece of telescope.
Concavo-convex lens: If one surface of convex lens is convex and the other is concave then it is called concavo convex lens. It is used in spectacles.
Double-concave lens: It both the surfaces of concave lens are concave then the lens is called double concave lens.
Plano-concave lens: If one surface of concave lens is plane and the other is concave then if is called plano-concave lens.
Convexo-concave lens: If one surface of concave lens is concave and the other is convex then if is called convexo-concave lens.
Focal plane of lens: The plane passing through principal focus of a lens and perpendicular to the principal axis of the lens is known as the focal plane of the lens.
Centre of curvature: The spherical surface of a lens is a part of sphere. The centre of the sphere is known as centre of curvature of the surface of lens.
Principal axis of a convex lens: The line joining the centres of curvature of the two spherical surfaces of a convex lens is called its principal axis.
Redius of curvature: Radius of curvature of a lens is the radius of the glass sphere from which the surfaces of the lens are cut.
Focus of convex lens : It a beam of parallel rays, travelling parallel to the principal axis of a convex lens are refracted by the lens, the rays became converging and intersect each other at a particular point on the axis. The point is known as the focus of the convex lens.
Optical centre: It a ray of light strikes one surface of a lens in such a way that emergent ray from the other surface is parallel to it, then the corresponding, refracted ray passed through a definite point on the principal axis. The point is the optical centre of the lens.
Focal length: The distance between the optical centre and the focus is known as focal length.
Formation of image by a lens:
- A ray parallel to the principal axis would pass through the second focus in case of a convex lens or appear to diverge from the second focus in case of a concave lens.
- A ray passes through optical centre of the lens undeviated.
- A ray actually passing through the first focus in case of convex lens or appearing to diverge from the first focus in case of concave lens comes out of the lens parallel to the principal axis.
Location of images formed for both types of lenses in different cases:
Object placed in infinity, the image is real, inverted, diminished and formed at the focus in the focal plane (fig. 5.8)
In (fig 5.9) is shown the position of image formed by a convex lens due to an object between 2 f and the infinity. The image is formed in between f and 2 f and real, inverted and diminished.
The situation for an object at a distance of 2 f is shown in (fig 5.10). The image is real, inverted of equal is size to the object and formed at a distance of 2 f from the lens.
In (fig 5.11) is shown the position of the image formed by a convex lens when the object lies between 2 f and f. The image is real, inverted and magnified.
In (fig 5.12) is shown when the object is situated at the focus of the convex lens. The image is real, inverted, highly magnified and is situated at infinity.
In (fig 5.13) is shown when the object is situated at a position less than the focal length of the convex lens. The image is erect virtual and magnified.
It can be shown in the case of a concave lens image is always erect, diminished and virtual [fig(g).]. As the object from infinity towards the lens, the image moves from the focus towards the lens.
Human eye: Human eye can be treated as a natural optical camera. It is nearly spherical in shape having following principal parts.
- Cornea
- Iris
- Pupil
- Lens
- Retina
- Ciliary muscles
- Optic nerve.
Working of eye :
The working of eye is similar to that of a Camera. In eye the amount of light entering it is adjusted by the iris, like the shutter in camera. The size of the opening of the pupil is changed by ciliary muscles. In a camera focussing of image is done by moving the lens forward or backward, while in human eye its focal length is changed by changing its shape by muscular effort.
The eye lens which is a convex lens forms a real, inverted image on the retina of the eye. The retina contains cells of the shape of rods and cones, which convert light energy into electrical signals and carried to brain through optic nerves. These signals are interpreted by the brain and we are able to see the object.
Accomodation of eye : The process by which ciliary muscles change the focal length of the eye lens so that a sharp image of the object at any distance from the eye is formed on the retina is called accomodation of eye.
Range of normal eye : The range of a normal eye varies from 25 cm to infinity.
Near point : The nearest point from an eye at which an object can be placed to see its sharp image is near point. (25 cm).
Far point: The farthest point from an eye at which an object can be placed to see its sharp image is called far point. For a normal eye the far point is infinity from the eye.
Power of accomodation : For a normal eye, the power of accomodation is about 4D (dioptre).
Defects of vision and their corrections : The common defects of human eye are –
Myopia (short-sightedness) : The defect where far point is less than infinity is known as myopia.
For correction of a myopia eye a concave lens of focal length-d is to be used. The power p of the lens is given by \(\frac{100}{f(\mathrm{in} \mathrm{cm})}\) dioptre.
Hypermetropia.(Long-sightedness): The defect where the near point moves away from 25 cm, but the eye can see distant objects without difficulty is called hypermetropia.
The defect can be corrected by using a convex lens of suitable focal length. Power of the lens \(\frac{100}{f(\text { in } \mathrm{cm})}\) dioptre
Presbyopia : The defect where an eye cannot see the near objects as well as distant objects clearly is called presbyopia.
To correct this defect bifocal lens of proper power and type is used with the lower one a convex lens to correct the near point and upper one a concave lens to correct the far point.
Astigmatism : The defect where an eye cannot focus horizontal and vertical lines simultaneously is known as astigmatism.
The cause of this defect is that the cornea of the eye has different curvatures in different directions.
Astigmatism is corrected by using a cylin-drical lens of suitable radius of curvature and suitable axis.
Prism: A prism is a portion of a transparent medium bounded by at least two plane faces inclined at suitable angle to each other.
Refraction through a prism
Angle of the prism
A = r1 + r2
Deviation produced
D = i1 + i2 – A
Minimum deviation : It is seen that the angle of deviation depends upon –
- angle of incidence
- angle of the prism
- Nature of the material of the prism
Dispersion of light : The phenomenon of splitting of a beam of white light into its constitutent colours is called dispersion of light.
Spectrum : The band of different colours obtained due to dispersion of white lens is known as a spectrum.
Cauchy’s formula : D = (μ-1) A
A prism only splite up the colours already present in white light and does not produce the colours.
The splitting of colours takes place at the first refracting surface of the prism only. In the second surface it is further refracted.
As all colours travel in vacuum with same speed, the material of the prism has same m for all the colours and so no dispersion takes place in vacuum.
The dispersion phenomenon is not exhibited by sound waves in air.
Scattering of light : The process of radiating light by atoms and molecules of the medium in all directions is called scattering of light.
Lord Rayleigh’s equation :
a = \(\frac{A V}{r \lambda^2}\)
\(I_s \propto \frac{1}{\lambda 4}\)(a = amplitude of scattered light at a distance r from the scattering particle in V volume. A = the amplitude of incident light of wave length λ.)
The intensity of scattered light varies inversely as the fourth power of the wavelength of the incident light-provided the size of the particles scattering light of very very small as compared to the wavelength of the incident light.
Some phenomena due to scattering of light
Blue colour of sky: \(I_s \propto \frac{1}{\lambda 4}\)
The intensity of the scattered blue light would be much more than that of the red colour. Thus in a clear sky, blue colour becomes prominent colour and the sky appears blue.
The clouds appear white
Reddish appearance of sun at sunrise and sunset.
Danger signals are red.
Pure spectrum: The spectrum in which the constituent coloums do not overlap an each other and are separated distinctly into elementary colours in known as a pure spectrum.
Impure spectrum: The spectrum in which the constituent colours partially superpose an each other and are not separated distinctly into elementary colours is known as impure spectrum.