CHAPTER - 10��

LIGHT : REFLECTION AND REFRACTION

PREPARED BY MS. REKHA CHOUDHARY T.G.T SCIENCE

K.V VIKASPURI

Light

• Light is a form of energy which enables us to see the objects.

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• When light falls on objects, it reflects the light and when the

reflected light reaches our eyes then we see the objects.

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• Light travels in straight line.

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• The common phenomena of light are formation of shadows,

formation of images by mirrors and lenses, bending of light by a

medium, twinkling of stars, formation of rainbow etc.

Reflection of light

When light falls on a highly polished surface like a mirror, most of

the light is sent back into the same medium. This process is called

reflection of light.

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• Laws of reflection of light :-

i) The angle of incidence is equal to the angle of reflection.

ii) The incident ray, the reflected ray and the normal to the mirror at

the point of incidence all lie in the same plane.

• Properties of image by Plane Mirror

• Always virtual ( cannot be obtained on a screen )
• Always erect
• Size is equal to that of the object.
• As far behind the mirror as the object is in front of it.
• Laterally inverted.

PREPARED BY MS. REKHA CHOUDHARY T.G.T SCIENCE

K.V VIKASPURI

• Spherical mirrors

Such mirrors , whose reflecting surfaces are spherical , are called spherical mirrors.

Spherical mirrors are of two types.

• Concave mirror
• Convex mirror.

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i) Concave mirror :- is a spherical mirror whose reflecting surface is curved inwards.

ii) Convex mirror :- is a spherical mirror whose reflecting surface is curved outwards.

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• Terms used in the study of spherical mirrors

• Pole :- is the centre of the reflecting surface of spherical mirror (P).

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• Center of curvature :- is the centre of the sphere of which the mirror is a part (C).

In case of concave mirror , it lies in front of it. In case of convex mirror, it lies

behind the mirror.

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• Radius of curvature :- is the radius of the sphere of which the mirror is a part (CP).

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• Principal axis :- is the straight line passing through the centre of curvature and the

pole (X-Y).

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• Principal focus :- In a concave mirror, rays of light parallel to the principal axis

after reflection meet at a point on the principal axis called principal focus(F).

In a convex mirror, rays of light parallel to the principal axis after reflection get

diverged and appear to come from a point on the principal axis behind the mirror

called principal focus (F).

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• Focal length :- is the distance between the pole and principal focus

(f). In a spherical mirror the radius of curvature is twice the focal

length.

R = 2f or f = R/2

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c F

X P Y

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C – Centre of curvature CP – Radius of curvature

P – Pole XY – Principal axis

F – Principal focus PF – Focal length

• Reflection by Spherical Mirrors

• In a concave mirror a ray of light parallel to the principal axis after reflection passes through the focus.
• In a convex mirror a ray of light parallel to the principal axis after reflection appears to diverge from the focus.

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C F P P F C

PREPARED BY MS. REKHA CHOUDHARY T.G.T SCIENCE

K.V VIKASPURI

• In a concave mirror a ray of light passing through the focus after reflection goes parallel to the principal axis
• In a convex mirror a ray of light directed towards the focus after reflection goes parallel to the principal axis.

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C F P P F C

• In a concave mirror a ray of light passing through the centre of curvature after reflection is reflected back along the same direction
• In a convex mirror a ray of light directed towards the centre of curvature after reflection is reflected back along the same direction.

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C F P P F C

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• In a concave or a convex mirror a ray of light directed obliquely at the pole is reflected obliquely making equal angles with the principal axis.

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i i

C F P P F C

r r

Image formation by concave mirror

• When the object is at infinity , the image is formed at the focus, it is highly diminished, real and inverted.

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C F P

PREPARED BY MS. REKHA CHOUDHARY T.G.T SCIENCE

K.V VIKASPURI

• When the object is beyond C, the image is formed between C and F, it is diminished, real and inverted.

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C F P

• When the object is at C, the image is formed at C, it is same size as the object, real and inverted.

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C F P

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• When the object is between C and F, the image is formed beyond C, it is enlarged, real and inverted.

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C F P

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• When the object is at F, the image is formed at infinity, it is highly enlarged, real and inverted.

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C F P

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• When the object is between F and P, the image is formed behind the mirror, it is enlarged, virtual and erect.

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C F P

Image formation by convex mirror

• When the object is at infinity, the image is formed at F behind the mirror, it is highly diminished, virtual and erect.

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P F

• When the object is between infinity and pole, the image is formed behind the mirror, it is diminished, virtual and erect.

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P F C

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Uses of spherical mirrors

• Concave mirrors
• Concave mirrors are used in torches, search lights and head lights of vehicles to get parallel beams of light.

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PREPARED BY MS. REKHA CHOUDHARY T.G.T SCIENCE

K.V VIKASPURI

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b) They are used as shaving mirrors to see larger image of the face.

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c) They are used by dentists to see larger images of the teeth.

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d) Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.�

• Convex mirrors

Convex mirrors are used as rear-view mirrors in vehicles. Because they give erect and diminished images of objects. They also have a wider field of view than plane mirrors.

• New Cartesian sign convention for spherical mirrors

• The object is always placed on the left of the mirror and light from the object falls from the left to the right.
• All distances parallel to the principal axis are measured from the pole.
• All distances measured to the right of the pole are taken as positive (+).
• All distances measured to the left of the pole are taken as negative (-).
• The height measured upwards perpendicular to the principal axis is taken as positive (+).
• The height measured downwards perpendicular to the principal axis is taken as negative (-).

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^{Direction of incident light}

^{Distance towards the left ( - ve )}

^{Distance towards the right ( + ve )}

^Height

^{downwards ( - ve )}

^Height

^{upwards ( + ve )}

^{Concave mirror}

^Object

^Image

• Mirror formula for spherical mirrors

The mirror formula for spherical mirrors is the relationship between the

object distance (u), image distance (v) and focal length (f).

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The mirror formula is expressed as :-

1 1 1

----- + ------ = ------

v u f

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PREPARED BY MS. REKHA CHOUDHARY T.G.T SCIENCE

K.V VIKASPURI

• Magnification for spherical mirrors

• It gives the relative extent to which the image of an object is magnified with respect to the object size.
• Magnification for spherical mirrors is the ratio of the height of the image to the height of the object.

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Height of the image hi

Magnification = --------------------------- m = -----

Height of the object h^o

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The magnification is also related to the object distance and image distance. It is expressed as :-

hⁱ v

Magnification m = ------ = (-)-------

h^o u

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*Height of object should be taken as positive.�*Height of image should be taken as positive for virtual � images.�*Height of image should be taken as negative for real � images.�*A negative sign in the value of magnification indicates � that the image is real.�*A positive sign in the value of magnification indicates � that the image is virtual.��

PREPARED BY MS. REKHA CHOUDHARY T.G.T SCIENCE

K.V VIKASPURI

• Refraction of light

• Light does not travel in same direction in all medium .
• When light travels obliquely from one transparent medium into another it gets bent. This bending of light is called refraction of light.
• Some common phenomena appears due to refraction of light such as-

-Bottom of a tank or a pond containing water appears to be raised

• When a thick glass slab is placed over some printed matter, the letters appear raised.
• A lemon kept in water in a glass tumbler appears to be bigger than its actual size when viewed from the sides.
• A pencil partly immersed in water in a glass tumbler appears to be displaced at the interface of air and water.
• Refraction is due to change in the speed of light as it enters from one transparent medium to another.

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• When light travels from a rarer medium(speed of light is higher than other medium) to a denser medium ( speed of light is less than other medium ), it bends towards the normal.
• When light travels from a denser medium to a rarer medium to a rarer medium, it bends away from the normal.

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^{Denser medium}

^{Rarer medium}

^{Rarer medium}

^{Denser medium}

Normal

Normal

• Refraction of light through a rectangular glass slab

When a ray of light passes through a rectangular glass slab, it gets bent twice at the air- glass interface and at the glass- air interface.

The emergent ray is parallel to the incident ray and is displaced through a distance.

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^e

^Normal

^{Incident ray}

^{Emergent ray}

^{Refracted ray}

^Glass

^Air

^Normal

^r

^Glass

^Air

Rectangular glass slab

displacement

Angle of emergence

Angle of incidence

Angle of refraction

• Laws of Refraction of Light

1. The incident ray , the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
2. The ratio of sine of angle of incidence to the sine of angle of refraction is a constant for the light of a given colour and for the given pair of media.(Snell law of refraction)

sin i = constant

sin r

This constant value is called the refractive index of the second medium with respect to the first.

• The Refractive Index

• A ray of light will change its direction when travels from one transparent medium into another medium.
• The extent of the change in direction that takes place in a given pair of media is expressed in the terms of refractive index.
• Consider a ray of light travelling from medium 1 into medium 2, then the refractive index of medium 2 with respect to medium 1 is given by the ratio of the speed of light in medium 1 and speed of light in medium 2.

n21 = speed of light in medium 1 = v1

speed of light in medium 2 v2

• The refractive index of medium 1 with respect to medium 2 is represented as n12.

n12 = speed of light in medium 2 = v2

speed of light in medium 1 v1

• If medium 1 is vacuum or air , then the refractive index of medium 2 is called the absolute refractive index of the medium. It is represented as n2.
• nm = speed of light in air = c

speed of light in the medium v

• The value of refractive index is helpful to compare the speed of light in different medium.
• In comparing the two different medium, the one with the large refractive index is denser medium than the other i.e. speed of light is less as compared to other medium.

• Spherical lenses

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A spherical lens is a transparent material bounded by two surfaces one or both of which are spherical.

Spherical lenses are of two main types.

i) Convex lens :- is thicker in the middle and thinner at the edges. Rays of light parallel to the principal axis after refraction through a convex lens meet at a point (converge) on the principal axis.

ii) Concave lens :- is thinner in the middle and thicker at the edges. Rays of light parallel to the principal axis after refraction get diverged and appear as come from a point on the principal axis on the same side of the lens.

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F F

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• Refraction by spherical lenses

• In a convex lens a ray of light parallel to the principal axis after refraction passes through the focus on the other side of the lens.
• In a concave lens it appears to diverge from the focus on the same side of the lens.

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2F₁ F₁ O F₂ 2F₂ 2F₁ F₁ O F₂ 2F₂

PREPARED BY MS. REKHA CHOUDHARY T.G.T SCIENCE

K.V VIKAPURI

• In a convex lens a ray of light passing through the focus after refraction goes parallel to the principal axis.
• In a concave lens a ray of light directed towards the focus after refraction goes parallel to the principal axis.

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2F₁ F₁ O F₂ 2F₂ 2F₁ F₁ O F₂ 2F₂

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• In a convex lens and concave lens a ray of light passing through the optical centre goes without any deviation.

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2F₁ F₁ O F₂ 2F₂ 2F₁ F₁ O F₂ 2F₂

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• Image formation by convex lens

• When the object is at infinity the image is formed at the focus F₂, it is highly diminished, real and inverted.

2F₁ F₁ O F₂ 2F₂

• When the object is beyond 2F₁, the image is formed between F₂ and 2F₂, it is diminished, real and inverted.

2F₁ F₁ O F₂ 2F₂

• When the object is at 2F₁, the image is formed at 2F₂, it is the same size as the object, real and inverted.

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2F₁ F₁ O F₂ 2F₂

• When the object is between 2F₁ and F₁, the image is formed beyond 2F₂, it is enlarged, real and inverted.

2F₁ F₁ O F₂ 2F₂

• When the object is at F₁ the image is formed at infinity, it is highly enlarged, real and inverted.

2F₁ F₁ O F₂ 2F₂

• When the object is between F₁ and O, the image is formed on the same side of the lens, it is enlarged, virtual and erect.

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2F₁ F₁ O F₂ 2F₂

• Image formation by concave lens

• When the object is at infinity, the image is formed at the focus F₁ on the same side of the lens, it is highly diminished, virtual and erect.

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F₁ O

• When the object is between infinity and F₁, the image is formed between F₁ and O on the same side of the lens, it is diminished, virtual and erect.

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F_I O

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• Sign convention for spherical lenses

The sign convention for spherical lenses is the same as in spherical mirrors except that the distances are measured from the optical centre (O).

The focal length of a convex lens is positive ( + ve ) and the focal length of a concave lens is negative ( - ve ).

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O

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^{Direction of incident light}

^{Distance towards the left (- ve )}

^Height

^{downwards ( - ve )}

^Height

^{upwards ( + ve )}

^{Convex lens}

^Object

^Image

^{Distance towards the right ( + ve )}

• Lens formula for spherical lenses

The lens formula for spherical lenses is the relationship between the object distance (u), image distance (v) and focal length (f).

The lens formula is expressed as :-

1 1 1

=

v u f

b) Magnification produced by spherical lenses :-

Magnification for spherical lens is the ratio of the height of the image to the height of the object.

Height of the image hⁱ

Magnification = m =

Height of the object h^o

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The magnification is also related to the object distance and image distance. It can be expressed as :-

hⁱ v

Magnification m = =

h^o u

• Power of a lens

It is the ability of lens to converge or diverge light rays.

The power of a lens is the reciprocal of its focal length (in metres).

1 1

P = or f =

f (m) P

The SI unit of power is dioptre (D).

1 dioptre is the power of a lens whose focal length is 1 metre.

The power of a convex lens is positive ( + ve ) and the power of a concave lens is negative ( - ve ).

PREPARED BY MS. REKHA CHOUDHARY T.G.T SCIENCE

K.V VIKASPURI