Posts
Diffraction of light - If an opaque object placed in the path of light is very small, then instead of traveling in a straight line, the light shows a tendency to bend at its edges. This effect of light is called diffraction of light.
Reflection of light : When light falls on polished and shiny surface, it bounces back in the same medium, this is called as reflection of light.
Laws of Reflection of light:
(i) The angle of incidence is equal to the angle of reflection.
∠ i = ∠ r
The incident ray, reflected ray and the normal all lie in the same plane.
Image formation by plane mirror :
1. The image formed by a plane mirror is virtual and erect.
2. The size of the image is equal to the size of the object
3. The image is formed at the same distance behind the mirror as the object is in front of it
4. The image formed by plane mirror is laterally inverted.
Lateral inversion : An image formed by a mirror the left of the object appears on the right and the right appears on the left. This is known as lateral inversion.
Spherical mirror
Such mirrors whose reflecting surface is curved inwards or outwards (spherical) are called spherical mirrors. There are two types of spherical mirrors.
1. Concave mirror - A spherical mirror, whose reflecting surface is curved inwards, called a concave mirror.
2. Convex mirror- A spherical mirror whose reflecting surface is curved outwards, is called a convex mirror.
Terms related to spherical mirror
1. Pole (P) – The center point of the reflecting surface of the spherical mirror is called the pole.
2. Center of Curvature (C) – The centre of the sphere of which the reflecting surface of a spherical mirror iforms a part is called the centre of curvature.
The centre of curvature of a concave mirror lies in front of it. while,The centre of curvature of a convex mirror lies behind the mirror
3.Radius of Curvature (R) – The radius of the sphere of which the reflecting surface of a spherical mirror forms a part, is called the radius of curvature of the mirror.
4. Principal axis – An Imaginary line passing through the pole and the centre of curvature of a spherical mirror is called the principal axis.
5. Principal focus (F) –The point on the principal axis of the mirror, at which the light rays coming parallel to principal axis after reflection actually meet or appear to come from there is called principal focus
The rays of light coming parallel to the principal axis of the concave mirror meet which point on the principal axis after reflection is called the focus of the concave mirror.
The rays of light coming parallel to the principal axis of a convex mirror after reflection rays appear to reflected from at which point on the principal axis is called the focus of a convex mirror.
In concave mirror, the reflected light rays actually pass through the focus, so focus is real and in front of mirror. But in convex mirror, the reflected light rays do not actually pass through the focus, so focus is virtual and behind mirror.
6.Focus lentgh (f) - The distance between the pole and the principal focus of a spherical mirror is called the focal length is called the focal length.
7. Aperture - The diameter of the reflecting surface of spherical mirror is called its aperture is called the aperture of the mirror.
Relationship between the radius of curvature R, and focal lenth 'f'
The focal length 'f' of spherical mirror is equal to half of the radius of curvature 'R'
i.e. f = R/2
Or
The radius of curvature 'R' of spherical mirror is twice the focus length ;'f'.
i.e. R=2f
It means the principal focus of a spherical mirror lies midway between the pole and centre of curvature.
Image Formation by Spherical Mirrors
To know the position and nature of the image formed by a spherical mirror we draw ray diagrams.We consider any two of the following rays for locating the image.
(i) A ray coming parallel to the principal axis, passes through the focus after reflection in case of concave mirror, or appear to diverge from the principal focus in case of convex mirror.
(ii) A ray coming through the focus of a concave mirror or , a ray which is directed towards the focus of a convex mirror, becomes parallel to principal axis.
(iii) A ray coming through the centre of curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror, after reflection, is reflected back along the same path.
The light rays come back along the same path because the incident rays fall on the mirror along the normal to the reflecting surface.
(iv) A ray incident obliquely to principal axis, towards a point P on the concave or convex mirror is reflected obliquely, following the laws of reflection.
Image formation by Concave Mirror
1. Position of the object → At infinity
Position of the image → At the focus F
Size of the image → Highly diminished point-sized
Nature of the image → Real and inverted
2. Position of the object → Beyond C
Position of the image → Between F and C
Size of the image → Diminished
Nature of the image → Real and inverted
3. Position of the object → At C
Position of the image → At C
Size of the image → Same size
Nature of the image → Real and inverted
4. Position of the object → Between C and F
Position of the image → Beyond C
Size of the image → Enlarged
Nature of the image → Real and inverted
5. Position of the object → At F
Position of the image → At infinity
Size of the image → Highly enlarged
Nature of the image → Real and inverted
6. Position of the object → Between P and F
Position of the image → Behind the mirror
Size of the image → Enlarged
Nature of the image → Virtual and erect
Uses of concave mirror :
1. Concave mirrors are commonly used in torches, search-lights and
vehicles headlights to get powerful parallel beams of light.
2. Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.
3. Concave mirrors are used by dentists to see large images of the teeth.
4. A concave mirror is used as saving mirror to see a larger image of the face.
Image formation by a Convex Mirror
1. Position of the object → At infinity
Position of the image → At the focus F behind the mirror
Size of the image → Highly diminished, point-sized
Nature of the image → Virtual and erect
2. Position of the object → Between iinfinity and the pole P of the mirror
Position of the image → Between P and F,behind the mirror
Size of the image → Diminished
Nature of the image → Virtual and erect
Uses of convex mirrors
1. Convex mirrors are commonly used as rear-view (wing) mirrors in vehicles.
2. Convex mirrors are placed near the ATM machine for security
Convex mirrors are preferred for drivers, because they always give an erect image. Also, they have a wider field of view as they are curved outwards. Thus, convex mirrors enable the driver to view much larger area than would be possible with a plane mirror.
Sign Convention for Reflection by Spherical Mirrors
(i) The object is always placed to the left of the mirror.
(ii) All distances parallel to the principal axis are measured from the pole of the mirror.
(iii) All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along – x-axis) are taken as negative.
(iv) Distances measured perpendicular to and above the principal axis
(along + y-axis) are taken as positive.
(v) Distances measured perpendicular to and below the principal axis
(along –y-axis) are taken as negative.
Mirror Formula
f = focal length of the mirror
u = distance of the object from the mirror
v = distance of the image from the mirror
Refraction of light
When a ray of light enters from one medium to another, it deviates from its original path at the separating plane of both the medium, this phenomenon is called refraction of light.
When light enters from one medium to another, there is a change in the velocity of light, due to change in velocity, refraction takes place.
Example
The bottom of a tank or a pond containing water appears to be raised.
A partially immersed pencil appears bent
A large coin appears raised in a glass
laws of refraction
1. Incident ray, refracted ray and normal all three lie in the same plane.
2. Snell's law - In refraction, the ratio of the sine of the angle of incidence (sin i) and the sine of the angle of refraction (sin r) always remains constant, it is called Snell's law.
Refraction through a Rectangular Glass Slab
Draw the outline of the slab with a pencil on paper sheet and give the name the outline as ABCD. Fix two pins on point E and F, vertically such that the line joining the pins is inclined to the edge AB. ook for the images of the pins E and F through the opposite edge and fix two other pins on point G and H, such that these pins and the images of E and F lie on a straight line. Remove the pins and the slab.and Join the point E and F and produce the line up to AB. Let EF meet AB at O. Similarly, join the point G and H and produce the line up to CD. Let HG meet CD at O'. Join O and O'. Also produce EF up to P, by a dotted line. In this Activity, we will note, the light ray has changed its direction. Draw a perpendicular NN’ to AB at O and another perpendicular MM' to CD at O'. The light ray at point O has entered from a rarer medium to a denser medium, that is, from air to glass. Note that the light ray has bent towards the normal. At O', the light ray has entered from glass to air, that is, from a denser medium to a rarer medium. The light here has bent away from the normal. Ray EO is incident ray on surface AB. OO' is the refracted ray and O' H is the emergent ray. The emergent ray is parallel to the incident ray. Extent of bending of the ray of light at the opposite parallel faces AB (air-glass interface) and CD (glass-air interface) of the rectangular glass slab is equal and opposite. This is why the emergent ray is parallel to the incident ray.
The Refractive Index
If the speed of light in medium 1 is v₁ and the speed of light in medium 2 is v₂ 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 the speed of light in medium 2.
This is usually represented by the symbol n₂₁
By the same argument, the refractive index of medium 1 with respect to medium 2 is represented as n₁₂.
If medium 1 is vacuum or air, then the refractive index of medium 2 is considered with respect to vacuum. This is called the absolute refractive index of the medium.
The ratio of the speed of light in vacuum or air and the speed of light in any medium is called refractive index.
Light travels fastest in vacuum with speed of 3×108 m s–1. In air, the speed of light is only marginally less, compared to that in vacuum. It reduces considerably in glass or water.
The medium of higher refractive index is optically denser medium. while the medium of lower refractive index is optically rarer medium. The speed of light is higher in a rarer medium than a denser medium. Thus, a ray of light travelling from a rarer medium to a denser medium slows down and bends towards the normal. When it travels from a denser medium to a rarer medium, it speeds up and bends away from the normal.
lens : A transparent medium bounded by two surfaces of which one or both surfaces are spherical is lens. There are two types of lenses.
1. Convex lens- Convex lens is thinner at the edges and thicker in the middle.Convex lens converges the rays of light after refraction, hence it is also called converging lens.
2. Concave lens - Concave lens is thicker at the edges and thinner in the middle. Concave lens diverges (spreads) the rays of light after refraction, hence it is also called diverging lens.
Terms related to spherical lens
1. Center of curvature - The centers of the two imaginary spheres of which the lens is formed are called centers of curvature.
3. Principal axis - The imaginary line passing through the two centers of curvature of a lens is called the principal axis.
4. Optical center : -The centre point of a lens is known as its optical centre. A ray of light through the optical centre of a lens passes without suffering any deviation
5. Radius of curvature: The distance between the centre of curvature and the optical centre of a lens is called the radius of curvature.
6. Aperture : The effective diameter of the circular outline of a spherical lens is called its aperture.
7. Focus distance- The distance between the optical center and the principal focus of the lens is called the focus distance.
8. Principal focus : The point on the principal axis of a lens where the rays of light coming parallel to the principal axis meet or appear to meet after refraction is called principal focus of lens. a lens has two principal foci. They are represented by F1 and F2.
Image Formation in Lenses Using Ray Diagrams
(i) A ray of light comig from the object, parallel to the principal axis, after refraction from a convex lens, passes through the principal focus on the other side of the lens. In case of a concave lens, the ray appears to diverge from the principal focus located on the same side of the lens
(ii) A ray of light passing through a principal focus or appear to meet at the principal focus, after refraction from a lens, emerges parallel to the principal axis.
(iii) A ray of light passing through the optical center of the lens emerges straight without any deviation.
Image Formation by convex Lenses
1. Position of the object →At infinity
Position of the image → At focus F2
Relative size of the image →Highly diminished,point-sized
Nature of the image →Real and inverted
2. Position of the object →Beyond 2F1
Position of the image → Between F2 and 2F2
Relative size of the image →diminished
Nature of the image →Real and inverted
3. Position of the object →At 2F1
Position of the image → At 2F2
Relative size of the image →Same size
Nature of the image →Real and inverted
4. Position of the object →Between F1 and 2F1
Position of the image → Beyond 2F2
Relative size of the image →Enlarged
Nature of the image →Real and inverted
5. Position of the object →At focus F1
Position of the image → At infinity
Relative size of the image → Infinitely large or highly enlarged
Nature of the image → Real and inverted
6. Position of the object → Between focus F1 and optical centre O
Position of the image → On the same side of the lens as the object
Relative size of the image → Enlarged
Nature of the image → Virtual and erect
Image Formation by concave Lenses
1. Position of the object → At infinity
Position of the image → At focus F1
Relative size of the image → Highly diminished, point-sized
Nature of the image → Virtual and erect
2. Position of the object → Between infinity and optical centre O of the lens
Position of the image → Between focus F1 and optical centre O
Relative size of the image → Diminished
Nature of the image → Virtual and erect
Lens Formula
f = focal length of the lens
u = distance of the object from the lens
v = distance of the image from the lens
Magnification : Magnification is the ability of a lens or mirror to magnify an object . The ratio of the height of the image to the height of the object is called magnification.
The magnification m is also related to the object distance (u) and image distance (v).
The height of the object is taken to be positive as the object is usually placed above the principal axis. The height of the image is taken as positive for virtual images and negative for real images. So negative sign in the value of the magnification indicates that the image is real and positive sign in the value of the magnification indicates the image is virtual.
Power of a Lens : The ability by of a lens converge or diverge light rays is expressed in terms of its power. The reciprocal of the focal length (f) of a lens is called the lens power. Its unit is diopter (D)
1 diopter is the power of a lens whose focal length is 1 meter.
The lens power of a convex lens is positive and a concave lens is negative.
- How many images are formed by two parallel mirrorsThe images formed by two parallel plane mirrors will be infinite.
- What is the radius of curvature of a plane mirror?The radius of curvature of a plane mirror is infinite.
- Name a mirror that can give an erect and enlarged image of an object.Concave mirror
- Write down four important characteristics of image formed by a plane mirror ?Image is virtual, erect, laterally inverted and of same size as object.
- The radius of curvature of a spherical mirror is 20 cm. What is its focal length ?Focal length f =R/2 = 20/2 = 10cm
- Define the Focal length of the spherical mirror ?The distance between focus and pole of a mirror is the focal length of the mirror.
- The refractive index of diamond is 2.42. What is the meaning of this statement?The refractive index of diamond, nd = 2.42 This means that the ratio of the speed of light in air and the speed of light in diamond is equal to 2.42.
- Define aperture of the spherical mirror ?The diameter of the reflecting surface of spherical mirror is called the aperture of the mirror.
- What do you mean by the pole of a spherical mirror?The center point of the reflecting surface of the spherical mirror is called the pole.
- Define principal axis of the spherical mirror ?An Imaginary line passing through the pole and the centre of curvature of a spherical mirror is called the principal axis.
- What is the center of the curvature of a spherical mirror?The centre of the imaginary sphere of which the mirror is part is called the centre of curvature.
- What are the advantages and disadvantages of using a convex mirror for seeing traffic at the rear?Advantage of Convex Mirror: It provide wider view of the rear traffic.Disadvantage: It does not give the correct distance of the vehicle at the rear.
- Define principal focus of a spherical mirror.The point on the principal axis, at which the incident rays which are parallel to principal axis meet or appear to diverge after reflection is called principal focus of spherical mirror.
- Name the spherical mirror used as: Shaving mirror, Rearview mirror in vehicles and Search – lights.Shaving mirror -Concave mirrorRearview mirror in vehicles - Convex mirrorSearch-lights. - Concave mirror
- Light enters from air to glass having refractive index 1.50. What is the speed of light in glass? Speed of light in air is 3 x108 m/s.
Speed of light in glass:
v = c= 3 x 10⁸
= 2 x 10⁸ m/s - Define the term reflection ?When a light ray falls on smooth polished surface such a mirror, the light bounce back in the same medium from it comes, this phenomena is known as reflection of light.
- State the laws of refraction of light “Or” State Snell’s law of refraction.
(i) Incident ray, refracted ray and normal to the point of incidence all three lie in the same plane.
(ii) Snell's law - In refraction, the ratio of the sine of the angle of incidence (sin i) and the sine of the angle of refraction (sin r) always remains constant, it is called Snell's law. - (a) Define real image of an object.
When the reflected rays after reflection actually meet at a point then real image is formed.
(b) Name the mirror that:
- can give real as well as virtual image of an object. - Concave mirror
- will always give virtual image of same size of an object. - Plane mirror
- will always give virtual and diminished image of an object. - Convex mirror
- is used by a doctor in examining teeth, - Concave mirror - Give the differences between a real and virtual image :
Real Image
Virtual Image
It can be taken on a screen
It can not be taken on a screen
It is always inverted
It is always erected
When reflected or refracted rays actually meet at a point, then
real image is formed.
When reflected or refracted rays appear to meet at a point then
virtual image is formed
- What is meant by radius of curvature of a spherical mirror? How is it related to the focal length of the mirror ?
The radius of the sphere of which the mirror is part, is called the radius of curvature of the mirror.
It is the distance between pole and centre of curvature of a mirror.
The radius of curvature 'R' of spherical mirror is equal to the twice the focal length R = 2f. - What is minimum number of rays required for locating the image formed by a concave mirror for an object? Draw a ray diagram to show the formation of a virtual image by a concave mirror.
We require minimum two rays for locating the image formed by a concave mirror. - Describe a spherical mirror ?
A spherical mirror is a mirror which has the shape of a piece cut out of a spherical surface. The reflecting surface of a spherical mirror is curved inside or outwards.There are two types of spherical mirrors.
Concave mirror - A spherical mirror, whose reflecting surface is curved inside, called a concave mirror. It is also called converging mirror
Convex mirror- A spherical mirror whose reflecting surface is curved outwards, is called a convex mirror. - Write two uses of concave mirror as well as convex mirror.Use of concave mirrors
In Vehicles headlights
As saving mirror
Use of convex mirror:
Convex mirrors are commonly used as rear-view (wing) mirrors in vehicles.
Convex mirrors are placed near the ATM machine for security - The refractive indices of three media are given below:
Medium Refractive Index
A 1.6
B 1.8
C 1.5
A ray of light is travelling from A to B and another ray is travelling from B to C.
(a) In which of the two cases the refracted ray bends towards the normal?
When light travels from an optically rarer medium to an optically denser medium it moves towards the normal. Since nB > nA hence the light ray will bend towards the normal on passing from medium A to B.
(b) In which case does the speed of light increase in the second medium? Give reasons for your answer.
The speed of the light will increase when the light travels from B to C, Since nc<nB and v=(c/n), the speed of light ray will increase in the second medium. - Define absolute refractive index.Absolute refractive index of a medium is the ratio of speed of light in air/vacuum to the speed of light in medium.
- With the help of ray diagram show that angle of incidence is equal to the angle of reflection when a ray is incident on the concave/convex mirror.
- With the help of a ray diagram, show that the formation of the image of an object by a concave mirror when it is placed at the centre of curvature.
- Draw a ray diagram for the image formed by a concave mirror when the object is placed beyond its centre of curvature (between centre of curvature and infinity for a concave mirror.)
OR
For what position of the object does a concave mirror form a real, inverted and diminished image of the object? Draw the ray diagram
In case of a concave mirror, when the object is placed beyond 2F(C) then image formed is real, inverted and diminishe - Draw a ray diagram in each of the following cases to show the position and nature of the image formed when object is placed:
(i) between focus and centre of curvature of a concave mirror.
(ii) between focus and pole of a concave mirror. - If the image formed by a spherical mirror for all positions of the object placed in front of it, is always erected and diminished, what type of mirror is it? Draw a labelled ray diagram to support your answer.
It is a convex mirror. Ray diagram for any position of object. - With the help of a ray diagram explain the use of concave mirror as solar concentrators.
The rays coming from the sun are parallel to principal axis and will concentrate at focus after reflection. - (a) Name the type of mirror used in the following:
Solar furnace - Concave mirror
Side/rear - view mirror of a vehicle. - Convex mirror
(b) Draw a labelled ray diagram to show the formation of image in each of the above two cases.
(c) Which of these mirrors could also form a magnified and virtual image of an object? Illustrate with the help of a ray diagram.
Concave mirror form magnified virtual image of an object. - Under what condition, a concave mirror produces a virtual and magnified image?
Draw a labelled ray diagram to show the formation of image in the above case.
Also, state the position of object to produce magnified and real image.
A concave mirror will produce a virtual and magnified image of the object if placed in between F and pole of the mirror. - Real and magnified image will be formed if the object is placed in between C and F in front of a concave mirror.
- A ray of light moving along principal axis is falling on a concave mirror. Draw the path of reflected ray. Also, state the values of angle of incidence and reflection in this case.
Ray of light moving along the principal axis will retraces it path because incident angle = reflected angle = 0 - Draw ray diagrams for the following cases when a ray of light:
(i) Passing through centre of curvature of a concave mirror is incident on it.
(ii) Parallel to principal axis is incident on convex minor.
(iii) is incident at the pole of a convex mirror.
(iv) passing through focus of a concave mirror incident on it. - (a) Complete the following ray diagram to show the formation of image.
(b) Mention the nature, position and size of the image formed in this case.
fffff
(c) State the sign of the image distance in this case using the Cartesian sign convention.
ffffff - Draw the following diagram, in which a ray of light is incident on a concave convex mirror, on your answer sheet. Show the path of this ray, after refl ection, in each case.
- An object of height h is kept at point P in front of a mirror as shown below. The height of the image produced is h'. In the diagram, F is the focus and C is the centre of curvature.
- The path of a light ray from three different media A, B and C for a given angle of incidence is shown below. Study the diagrams and answer the following questions
(i) Which of the three media A, B or C has maximum optical density?
Medium C is maximum optical denser.
(ii) Through which of the three media, will the speed of light be maximum?
In medium A the speed of light will be maximum
(iii) Will the light travelling from A to B bend towards or away from the normal?
Bend towards the normal
(iv)Will the refractive index of B relative to C be more than unity or less than unity?
Less than 1
Refractive index of turpentine oil, kerosene and alcohol are 1.47, 1.44 and 1.36 respectively. On the basis of this information, complete the following ray diagram to show path of ray of light through each medium. Give reason for your answer.
When a ray passes from optically rarer to denser medium it bends towards the normal . - (a) If the object is now moved to point C, will the height of the image now produced be less than, equal to, or greater than h'? Give a reason for your answer.
The height of the image produced when the object is at C will be less than h'. The magnification is more when the object is at point P than at C.
(b) If the focal length of the mirror is 20 cm and the distance between points P and C is 10 cm, determine the distance between the images produced when the object is kept at P and C.
When the object is kept at P :
u = -30 cm
f = - 20 cm
v₁ = -60 cm
When the object is kept at C
Since C is the centre of curvature, image distance = object distance
v₂ = -40 cm
Distance between the images = v₂ - v₁
= 60 - 40
= 20 cm - Absolute refractive index of medium A and medium B are na and nb respectively, what is the refractive index of medium B with respect to medium A? How does the velocity of light vary with change in the optical density of the media?
Higher the optical density, lesser is the velocity of light in the medium - (a) Water has refractive index 1.33 and alcohol has refractive index 1.36. Which of the two medium is optically denser? Give reason for your answer. Draw a ray diagram to show the path of a ray of light passing obliquely from water to alcohol.
More refractive index means more optical denser medium. Here refractive index of water is 1.33 and of alcohol is 1.36 nAl > nw Hence alcohol is more optical denser than water.
(b) The absolute refractive index of diamond is 2.42 and the absolute refractive index of glass is 1.50. Find the refractive index of diamond with respect to glass. - As the velocity of light increases, the refractive index of the medium decreases. Light enters from air to water having refractive index 4/3. Find the speed of light in water. The speed of light in vacuum is 3x108 m/s.]
Given nw = 4/3
c= 3x108 m/s.]
vw = ?
