Light-Reflection and Refraction
Light:
• Light travels in a straight line.
• A highly polished surface such as mirror reflects most light falling on it.
• A plane mirror is a flat surface that reflects light.
•The spherical mirrors have a curve like surface so they are known as curred mirror.
i. Pole
ii) A ray of light passing through the principal focus of concave mirror or a ray of light which is directed towards the focus of convex mirror emerge/becomes parallel to the principal focus after reflection.
iii) A light ray that passes through the centre of curvature of a concave mirror or directed in the direction of the centre of curvature of convex mirror is reflected back alone the same path or retraces its path after reflection.
iv) A ray of light incident on the pole of concave or convex mirror gets reflected at the same angle on the other end of the principal axis of the mirror.
Formation of image by Concave Mirror:
Position of image: At the focus (F).
Position of image: Between F and C
Position of image: At C
Position of image: Beyond C.
Position of image: Behind the mirror.
Position of image: At the focus (F)-Behind thr mirror.
Position of image: Between P and F-Behind the mirror.
(iii) It is used as shaving and makeup mirror to see a large image of face.
iv) Very large concave mirrors are used to focus/concentrate sunlight to produce heat in solar furnace.
Uses of Convex mirror:
According to the New Cartesian Sign Convention-
• It is a form of energy that enable us to see the things around us.
• When light falls on an object some of light is reflected towards us, this reflected light when enters/received by our eyes enable us to see the things.
• We are unable to see anything in a dark room or where there is no light.
• During the day sun is the natural source of light which helps us to see the things/objects.
Properties of Light:
• Light is electromagnetic wave which do not required any material medium to travel i.e It can travel in vaccum.
Note: The path of light changes only when there is an object in its path or when the medium changes.
• Light has dual nature i.e wave as well as particle nature.
• Light cast shade
• Light travels with very high speed and the speed of light is 3x10⁸ m/s or 299,792, 458 m/s.
Note: No material particle can travel at a speed greater than that of speed of light.
Reflection of light :
• The process/phenomenon of bouncing/sending back of light rays into the same medium when fall/ strike on the surface is called Reflection of light.
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 surface/mirror at the point of incidence, all lie in the same plane.
• The ray of light which falls on the mirror surface is called the incidence ray.
• The ray of light which is sent back by the mirror is called reflected ray.
• The line which is perpendicular the mirror called normal.
• Any ray of light which is incident normally/perpendicularly on a mirror is reflected back along its own/same path.
Note: The Laws of reflection holds true / applicable to all types of reflecting surface including spherical mirror.
Some important terms:
Image:- It is a point where atleast two light rays actually meet or appear to meet.
Or
"The point of intersection of reflected ray is called image i.e the intersection of atleast two reflected rays give the position of the image of an object.
Types of Image
1. Virtual Image:- When light rays appear to meet then the image formed is virtual or an image which is not formed by the actual intersection of light rays and cannot obtained on screen called virtual image.
2. Erect Image:- The image formed in such a way that head at the top & the feet at the bottom called erect image.
Object:- Anything which gives light rays either its own or reflected by it called an object.
Or
Point of intersection of incident ray reflected by is called object.
Formation of Image by a plane mirror:
• Image formed by a plane mirror is always virtual & erect.
• The size of image formed by plane mirror is equal to size of object.
• The image formed in a plane mirror is as far behind as the object is in front of it i.e the image and the object are equidistance from the plane mirror.
• The size of image formed is equal to the size of the object.
• The Image formed is laterally inverted i.e left seems to be right and right seems to the left.
Spherical Mirrors:
•Such mirrors, whose reflecting surfaces are spherical are called spherical mirrors.
•The reflecting surface of a spherical mirror forms part of hollow sphere.
• The reflecting surface of spherical mirror may be curved inwards or outwards.
• Hence the spherical mirrors are special type of curved mirrors In which the surface of the mirror is a part of sphere.
Types of spherical mirror
The Spherical mirror is of two types:
1- Concave Mirror
• A spherical mirror, whose reflecting surface is curved/bulges inwards is called concave mirror.
• It converges the light so it is also called converging mirror.
Note:- The surface of the spoon curved inwards can be considered as a concave mirror.
2- Convex Mirror:
• A spherical mirror whose reflecting surface is curved / bulges outwards is called a convex mirror.
• It diverges the light so it is also called diverging mirror.
Note - The surface of the spoon bulged outwards can be considerd as a convex mirror.
Spherical Mirror Terms:
•The centre/mid point of the reflecting surface of a spherical mirror is called" Pole.
• It lies on the surface of mirror.
• It is represented by the letter (P).
(ii) Centre of Curvature:
• The centre of the hollow/ imaginary sphere of which the shperical mirror is a part is called the centre of curvature.
• It lies outside its reflecting surface.
• It is represented by letter (C).
• The centre of curvature of a concare mirror is in front of it but the centre of curvature of convex mirror is behind it.
Note: The centre of curvature is not part of mirror.
(iii) Radius of Curvature
• The radius of sphere of which the reflecting surfacr of spherical mirror is a part is called Radius of Curvature.
• It is represented by (R).
• It is the distance b/w centre of curvature & the spherical mirror.
iv) Principal axis:
• The Straight line joining / passing through the pole & the centre of curvature is called the poincipal axis.
• The principal axis is normal /perpendicular to the mirror at its pole.
v) Focus:
• A point on the principal axis of the mirror, where all the incident/coming rays paralled to the principal axis converge or diverge after reflection is called. focus.
• A concave mirror has a real focus.
• A convex mirror has a virtual focus.
• Focus lies b/w pole & centre of curvature.
vi) Focal Length:
• The distance between the pole and focus is called the focal length of the mirror.
• It is denoted bt the letter f.
vii) Aperture
• The aperture of the mirror represents the size of the mirror.
• The diameter of the reflecting surface of the spherical mirror is called its aperture.
Or
The portion of a mirror from which the reflecting of light actually takes place is called the aperture of the mirror.
Or
Circular area that determines the amount of light falling on a mirror is its aperture.
Relationship between radius of curvature (R) and focal length (f) of a spherical mirror:
• The focal length of a spherical mirror of small aperture is equal to half of its radius of curvature.
f = R/2 or R = 2f
Rules for making ray diagrams by spherical mirror:
i) A ray of light which is parallel to the principal axis passes through the principal focus in case of concave mirror or appear to diverge from the principal focus in case of convex mirror after reflection.
• The nature, position and size of the image formed by a concave mirror is depends on the position of the object w.r.to P, F and C in front of the mirror.
Case 1: When the object is at infinity.
Size of image: Highly diminished or pointed size.
Nature of image: Real and inverted.
Case 2: When the object is beyond C.
Size of image: Diminished
Nature of image: Real and inverted.
Case 3: When the object is at C.
Size of image: Same size as the object
Nature of image: Rela and inverted.
Case 4: When the object is placed between F and C.
Size of image: Enlarged or magnified.
Nature of image: Real and inverted.
Case 5: When the object is placed at F.
Position of image: At infinity.
Size of image: Highly enlarged or magnified.
Nature of image: Real and inverted.
Case 6: When the object is placed between F and P.
Size of image: Enlarged.
Nature of image: Virtual and Erect.
Formation of image by convex Mirror:
Case 1: When the object is at infinity.
Size of image: Highly diminished or pointed size.
Nature of image: Virtual and Erect.
Case 2: When the object is placed between P and Infinity.
Size of image: Diminished.
Nature of image: Virtual and Erect.
Note: Convex mirror gives the full length of image of a large object like tall building or tall tree.
Uses of Concave mirror:
(i) It is used in torches, search lights and vehicles headlights to get powerful parallel beams of light.
(ii) It is used by the dentists to see the large images of the teeth of patients.
(1) Convex mirror are used as rear view mirrors in vehicles because it always gives an erect image & it have wider field of view.
(ii) Big convex mirrors are used as 'Shop security mirrors.
iii. Convex mirror is used as reflectors at sharp turns or blind turns.
Mirror Formula:
A formula which gives the relationship b/w image distance (v), object distance (u) & focal length (f) of a spherical mirror is known as the mirror formula.
The mirror formula can be written as:
1/f = 1/v + 1/u.
•Image distance- The distance of the image from the pole of the mirror is the image distance.
Object distance:~ The distance of an object from the pole of the mirror is called object distance.
Note: This formula can be applied to both type of spherical mirrors i.e concace & convex mirrors.
• By using this formula, we can find out the position & nature the images formed by concave & convex mirrors.
Magnification:
• The ratio of the height of image to the height of object is known as Linear magnification.
• It is usually represented by the Letter (m).
• "If 'h' is the height of the image and h is the height of the object, then the magnification (m) produced by a spherical mirror is given by -
m = h'/ h
The magnification (m) is also related to the object distance (u) & image distance (v) & expressed or given by /as:
m = h'/ h = -v/u.
• If the magnification value is -ve, then the image is real and Inverted.
• If the magnification value is +ve, then the image is virtual & erect.
• If `m` has value greater than 1 the image is bigger.
• If `m` has value less than 1 the image is diminished or small size.
• If `m` has value equal to 1 then the size of image will be equal to the size of an object.
Note: Magnification produced by a plane mirror is always 1 and the magnification produced by a concave mirror is always less than 1.
Sign Convention for Reflection by Spherical Mirror.
i) The pole (P) of the mirror is taken as the origin and all the distances parallel to the principal axis are measured from the pole of the mirror.
(ii) All the distances measured to the right side of the origin i.e along +x-axis are takes as +ve.
Or
Distances measured in the same direction as that of incident light are taken as -ve.
iii) All the distances measured to the left side of the origin i.e along -x-axis are takes as -ve.
Or
Distances measured against/opposite to the direction of incident light are taken as -ve.
(iv) Distances measured perpendicular and above / upward to the principal axis are taken or considerd as +ve along +y-axis.
v) Distances measured perpendiculer & below/ downward to the Principal axis are taken as -ve i.e along -y axis.
vi) The object is placed always on /to the left side of the mirror or origin.
Conclusions:
i) The object distance is always -ve for spherical mirrors (concave and convex) i.e u=-ve.
ii) Focal length of concave mirror is -ve i.e f=-ve.
And
Focal length of convex mirror is +ve i.e f=+ve.
iii) If an image is formed behind or to the right side to concave mirror then the image distance is taken as +ve i.e v=+ve.
And
If an Image is formed in front or left side to the concave image distance is taken as -ve i.e v=-ve.
Note: In a convex mirror, the image is always formed in the right side i.e behind the mirror, so the image distance in this case is always +ve i.e v=+ve.
iv) The height of an object is always +ve because it always placed above the principal axis i.e h=+ve.
v) If an image is formed above the principal axis, its height is taken as +ve i.e h2= +ve.
Or
If an image is formed below the principal axis, then its height is taken as -ve i.e h2= -ve.
Note: Height of all the virtual and erect images is taken as positive and Height of all the real and invited images is taken as negative.
Refraction of Light:
• The phenomena of bending/ change in direction of light when it passes/enters / goes from one transparent to another obliquely, is called refraction of light.
• The refraction of light is due to the change in the speed of light as it enters / on going from one mediend to another.
Note: If the incident ray falls normally (perpendicularly) to the refractive surface of a glass slab, then there in no bending of light rays (refracting) occurs, it goes straight.
Laws of Refraction of light :
1- The incident ray, the refracted ray and the normal to the interface of two transparent medium at the Point of incidence, all lie in the same plane.
2- The ratio of sine of angle of incidence to the sin of angle of refraction is constant for a given pair of media.
i.e sini/sinr = constant (This is also called "Snells Law").
Note: This constant value called the refractive index.
Refractive Index:
• The ratio of speed of light in a given pair of media is known as refractive Index.
• It is denoted by n.
• It has no unit i.e unitless.
n = speed of light in air or vaccum / speed of light in medium = v1/v2
• Consider a ray of light travelling from medium 1 with speed V1 to medium 2 with speed V2, Then the refractive index of medium 2 wrt medium 1 is given by the ratio of speed of light in medium 1 and the speed of light in medium 2 is represented as n21
n21 = speed of light in medium 1 / speed of light in medium 2 = v1/v2
• The refractive index of medium I w.r.to medium 2 is represented as n12
n12 = speed of light in medium 2 / speed of light in medium 1 = v2/v1
Absolute Refractive Index: -
• If medium 1 is vaccum/air, then the refractive index of medium 2 w.r.to vaccum is called the absolute refractive index of the medium.
• The Refractive index of a medium w. to air/vacuum is called the absolute refractive index.
• It is represented as n2.
• If c is the speed of light in air/vacuum and v is the speed of light in medium, then the refractive index of the medium nm is given by -
nm = Speed of light in air /Speed of light in medium=c/v
Note: The absolute refractive Index of a medium is called its refractive index.
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