CBSE Class 10 Science Light Reflection And Refraction Notes Set 03

These CBSE Class 10 Science notes for Chapter 9, Light – Reflection and Refraction, cover reflection and its laws, image formation by plane, concave and convex mirrors, the mirror formula and magnification, refraction of light and refractive index, refraction through a glass slab, image formation by convex and concave lenses, the lens formula, and the power of a lens. The ray diagrams are constructed from the mirror and lens formulae and each image position is summarised in a table.

Important Notes and Formulas

Reflection of Light

Reflection of light is the phenomenon of bouncing back of light in the same medium on striking the surface of any object. An object reflects the light that falls on it, and when this reflected light reaches our eyes we see the object.

There are two types of reflection:

1. Regular (specular) reflection: When the reflecting surface is smooth and well polished, the parallel rays falling on it are reflected parallel to one another, in one particular direction.
2. Irregular (diffuse) reflection: When the reflecting surface is rough, the parallel rays falling on it are reflected in different directions.

Laws of Reflection

1. The angle of incidence is equal to the angle of reflection (∠i = ∠r).
2. The incident ray, the normal to the mirror at the point of incidence and the reflected ray all lie in the same plane.

These laws apply to all types of reflecting surfaces, including spherical surfaces.

Luminous and Non-luminous Objects, Real and Virtual Images

1. Luminous objects emit their own light, for example the Sun, other stars, an electric bulb and a tubelight.
2. Non-luminous objects do not emit light themselves; they only reflect or scatter the light that falls on them, for example a flower, chair, table or book.
3. Image: An image is an optical appearance produced when light rays coming from an object are reflected from a mirror (or refracted through a lens).
4. Real image: The image that can be obtained on a screen. The rays actually meet at the image. A real image is always inverted. The image on a cinema screen is real.
5. Virtual image: The image that cannot be obtained on a screen. The rays only appear to meet when produced backwards. A virtual image is always erect. The image of our face in a plane mirror is virtual.

Image Formed by a Plane Mirror

1. The image of a real object is always virtual and cannot be taken on a screen.
2. The image is always erect.
3. The image is of the same size as the object (magnification +1).
4. The image is as far behind the mirror as the object is in front of it (the dashed distances d in the figure are equal).
5. The image is laterally inverted: the right side of the object appears as the left side of the image and the left side appears as the right side. This is called lateral inversion.

Spherical Mirrors

A spherical mirror is a mirror whose reflecting surface is a part of a hollow sphere of glass. There are two types:

1. Concave mirror: The reflecting surface is the inward curved (bent-in) surface. It is a converging mirror.
2. Convex mirror: The reflecting surface is the outward curved (bulging-out) surface. It is a diverging mirror.

1. Pole (P): the centre of the reflecting surface of the mirror.
2. Centre of curvature (C): the centre of the hollow sphere of which the mirror is a part.
3. Radius of curvature (R): the radius of that sphere, i.e. the distance PC.
4. Principal axis: the straight line passing through the pole and the centre of curvature.
5. Aperture: the diameter of the reflecting surface (MN in the figure).
6. Principal focus (F): for a concave mirror it is the point on the principal axis where rays parallel to the axis meet after reflection (real focus, in front of the mirror). For a convex mirror it is the point from which rays parallel to the axis appear to diverge after reflection (virtual focus, behind the mirror).
7. Focal length (f): the distance between the pole and the principal focus.

For mirrors of small aperture, the focal length is half of the radius of curvature: \( f=\dfrac{R}{2} \), that is, R = 2f.

Rules for Obtaining Images Formed by Spherical Mirrors

The intersection of at least two reflected rays gives the position of the image of a point on the object. Any two of the following rays can be used:

1. A ray parallel to the principal axis, after reflection, passes through the principal focus (concave mirror) or appears to diverge from the principal focus (convex mirror).
2. A ray passing through the principal focus of a concave mirror, or directed towards the principal focus of a convex mirror, after reflection emerges parallel to the principal axis.
3. A ray passing through the centre of curvature of a concave mirror, or directed towards the centre of curvature of a convex mirror, is reflected back along the same path, because it falls on the mirror along the normal.
4. A ray incident obliquely at the pole P of the mirror is reflected obliquely, making equal angles with the principal axis.

Image Formation by a Concave Mirror

The nature, position and size of the image formed by a concave mirror depend on the position of the object. The figures below are drawn for a concave mirror of focal length 10 cm.

Object at infinity

Object beyond C (u = −30 cm)

Object at C (u = −20 cm)

Object between C and F (u = −15 cm)

Object at F

Object between P and F (u = −5 cm)

Uses of Concave Mirrors

1. In torches, search-lights and vehicle headlights, to get powerful parallel beams of light.
2. As shaving mirrors, to see a larger image of the face.
3. By dentists, to see large images of the teeth of patients.
4. As doctors' head mirrors, to focus light on the body parts to be examined.
5. Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.

Image Formation by a Convex Mirror

Object at infinity

Object at a finite distance (u = −30 cm, f = +15 cm)

Uses of Convex Mirrors

Convex mirrors are commonly used as rear-view (wing) mirrors in vehicles. They always give an erect, though diminished, image, and because they are curved outwards they have a wider field of view. Convex mirrors therefore enable the driver to view a much larger area than a plane mirror would.

Sign Convention for Spherical Mirrors

1. The object is always placed to the left of the mirror, so that light from the object falls on the mirror from the left.
2. All distances are measured from the pole of the mirror, which is taken as the origin.
3. Distances measured in the direction of the incident light (to the right of the pole) are positive; distances measured against the incident light (to the left) are negative.
4. Distances (heights) measured upward and perpendicular to the principal axis are positive; those measured downward are negative.
5. As a result, the object distance u is always negative, the focal length of a concave mirror is negative and that of a convex mirror is positive.

Mirror Formula and Magnification

The relation between the object distance (u), the image distance (v) and the focal length (f) of a spherical mirror is the mirror formula: \( \dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f} \).

The magnification is the ratio of the height of the image to the height of the object: \( m=\dfrac{h'}{h}=-\dfrac{v}{u} \).

1. The height of the object is taken positive. The height of a virtual, erect image is positive and that of a real, inverted image is negative.
2. A negative value of m means the image is real and inverted; a positive value means the image is virtual and erect.
3. If |m| > 1 the image is enlarged, if |m| < 1 it is diminished and if |m| = 1 it is of the same size.
4. A convex mirror always gives m between 0 and +1, while a concave mirror can give positive or negative values.

Refraction of Light

The change in the direction of light when it passes obliquely from one transparent medium to another is called refraction of light. Refraction is caused by the change in the speed of light on going from one medium to another.

1. Optically rarer medium: a medium in which the speed of light is more.
2. Optically denser medium: a medium in which the speed of light is less.
3. When a ray goes from a rarer medium to a denser medium, it bends towards the normal.
4. When a ray goes from a denser medium to a rarer medium, it bends away from the normal.
5. A ray incident along the normal passes undeviated.

Laws of Refraction

1. The incident ray, the refracted ray and the normal to the interface of the two transparent media at the point of incidence all lie in the same plane.
2. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for light of a given colour and for the given pair of media: \( \dfrac{\sin i}{\sin r}=\text{constant} \). This is Snell's law, and the constant is the refractive index of the second medium with respect to the first.

Refractive Index

The absolute refractive index of a medium is the ratio of the speed of light in vacuum (or air) to the speed of light in the medium: \( n=\dfrac{c}{v} \), where c = 3 × 10⁸ m/s.

The refractive index of medium 2 with respect to medium 1 is \( {}_{1}n_{2}=\dfrac{n_2}{n_1}=\dfrac{v_1}{v_2} \), and \( {}_{1}n_{2}=\dfrac{1}{{}_{2}n_{1}} \). Refractive index has no unit.

A medium with a higher refractive index is optically denser, and light travels more slowly in it. For example, the refractive index of diamond is 2.42, which means the speed of light in diamond is 2.42 times less than in air.

Refraction Through a Rectangular Glass Slab

A ray of light passing through a rectangular glass slab suffers two refractions, one at the air–glass surface and the other at the glass–air surface. It emerges parallel to the direction of the incident ray (angle of emergence ∠e equals the angle of incidence ∠i) but is shifted sideways by a distance d, called the lateral displacement.

The lateral displacement increases with the thickness of the slab, with the angle of incidence and with the refractive index of the glass.

1. Refraction does not occur (the ray does not change direction) when light is incident normally on the boundary, because then i = 0° and r = 0°.
2. Refraction does not occur when the two media have the same refractive index, because then n₁ = n₂ and i = r.

Spherical Lenses

A transparent material bound by two surfaces, of which one or both are spherical, forms a lens.

1. Convex lens: bulges outwards on both sides; it is thicker at the middle than at the edges. It converges light rays and is called a converging lens.
2. Concave lens: curved inwards on both sides; it is thicker at the edges than at the middle. It diverges light rays and is called a diverging lens.

1. Principal axis: the imaginary straight line passing through the two centres of curvature of the lens.
2. Optical centre (O): the central point of the lens. A ray passing through it goes undeviated.
3. Centres of curvature (C₁, C₂): the centres of the two spheres of which the lens surfaces are parts.
4. Aperture: the effective diameter of the circular outline of the lens.
5. Principal focus (F): for a convex lens, the point on the principal axis where rays parallel to the axis converge after refraction; for a concave lens, the point from which they appear to diverge. A lens has two foci, F₁ and F₂, at equal distances on either side of O.
6. Focal length (f): the distance between the optical centre and the principal focus.

Rules for Obtaining Images Formed by Spherical Lenses

1. A ray parallel to the principal axis, after refraction, passes through the principal focus on the other side of a convex lens, or appears to diverge from the principal focus on the same side of a concave lens.
2. A ray passing through the principal focus of a convex lens, or appearing to meet at the principal focus of a concave lens, emerges parallel to the principal axis.
3. A ray passing through the optical centre emerges without any deviation.

Image Formation by a Convex Lens

Object at infinity

Object beyond 2F₁ (u = −30 cm)

Object at 2F₁ (u = −20 cm)

Object between F₁ and 2F₁ (u = −15 cm)

Object at F₁

Object between F₁ and O (u = −5 cm)

Image Formation by a Concave Lens

Object at infinity

Object at a finite distance (u = −30 cm, f = −15 cm)

Sign Convention for Spherical Lenses

1. All distances are measured from the optical centre of the lens.
2. Distances measured in the direction of the incident light are positive and those measured against the incident light are negative.
3. Heights measured upward and perpendicular to the principal axis are positive and those measured downward are negative.
4. The focal length of a convex lens is positive and that of a concave lens is negative. The object distance u is always negative.
5. The distance of a real image is positive and that of a virtual image is negative.

Lens Formula and Magnification

The lens formula relates the object distance (u), the image distance (v) and the focal length (f): \( \dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f} \).

The magnification produced by a lens is \( m=\dfrac{h'}{h}=\dfrac{v}{u} \).

1. A positive m means a virtual and erect image; a negative m means a real and inverted image.
2. A convex lens can form real as well as virtual images, so its magnification can be negative or positive, and its value can be less than 1, equal to 1 or more than 1.
3. A concave lens always forms a virtual, erect and diminished image, so its magnification is always positive and less than 1.

Power of a Lens

The power of a lens is the reciprocal of its focal length: \( P=\dfrac{1}{f} \), where f is in metres. The SI unit of power is the dioptre (D). One dioptre is the power of a lens whose focal length is 1 metre (1 D = 1 m⁻¹). The power of a convex lens is positive and that of a concave lens is negative.

When lenses are placed in contact, the net power is the algebraic sum of the individual powers: P = P₁ + P₂ + P₃ + … The corresponding magnification of a combination is the product of the individual magnifications.

Summary of Formulas