Light - Reflection and Refraction
What is light?
- Light is a form of energy which enable us to see things around us.
- Light travels along straight path
- Speed of light is measurable (3x10^8 m/s) in vaccum
- It is an electromagnetic wave, so does not require any medium to travel.
- Light cast shadow
- When light falls on a surface , following may happen
- -reflection
- -refraction
- -Absorption
Ray of light:-
- Straight line path of light
- Beam of light:-
- Bunch of rays of light
Reflection of light:-
- Bouncing back of light into the same medium when it strikes a boundary between different media through which it cannot pass.
- Or bouncing back of light when it strikes on a polished surface like mirror.
Laws of Reflection:-
1. Angle of incidence is equal to angle of Reflection .
2. Incident ray , reflected rah and the normal all lie in the same plane.
Spherical mirror:-
Part of reflective spherical sphere.
Or
Mirror whose reflecting surface is curved.
Types:- two types
Concave :- whose reflecting surface is on inside the sphere
Convex:- whose reflecting surface is outside the sphere.
Terminology:-
Pole:- centre of reflecting surface/spherical motor
Centre of curvature (C):- Centre of sphere of which mirror is a part.
Radius of curvature(R):- Radius of sphere of which mirror is a part.
Principal Axis:- Line joining pole with centre of curvature
Principal Focus(F):-
Point on principal Axis where the rays of light incident on mirror parallel to principal Axis converge or appear to diverge.
Concave mirror is also called converging mirror why?
This is because all the light rays coming parallel to principal Axis converge at a point called principal focus after reflection . That's why it is called converging mirror.
Convex mirror is also called diverging mirror . Why ?
This is because all the light rays coming parallel to principal Axis appear to diverge from a point called principal focus after reflection. ThstaT why it is called diverging mirror
Relationship between R and f is R= 2f
Characteristics of image formed by plane mirror:-
- 1. Virtual and erect
- 2. Size of image is equal to size of object.
- 3. Image is formed as far behind the mirror as the object is in front of it .
- 4. Lateral inverted.
Lateral inversion:- The right side of object appear left side of the image and vice versa.
Application of lateral inversion:-The word AMBULANCE so that it can be read correctly in rear view mirror of vehicle going in front of it.
Real image :-
- Formed when light rays actually meet.
- Inverted
- Example:- Image formed by concave mirror.
Virtual image:-
- Formed when light rays appear to meet .
- Erect
- Example:- image formed by plane mirror or convex mirror
Representation of image formed by spherical mirrors using ray diagrams:-
Rule 1 :- Whenever a ray of light is incident on the mirror parallel to the principal Axis ,it passed through principal Focus.
Rule 2:- A ray of light which passed through the principal Focus toward the spherical mirror after reflection is reflected parallel to principal Axis.
Rule 3:- A ray of light which passed through the centre of curvature of a spherical mirrim after reflection retraces the same path ,i.e goes back along the same path
Rule 4:- A ray of light which is incident towards the pole of spherical mirror obliquely to the principal Axis is reflected obliquely.
Ray diagrams for images formed. by concave mirror :-
1. Position of object:- At infinity
Position of image:- At F
Nature of image:- Real and inverted
Size of image:- point sized or highly diminished
2.Position of object:- beyond C
Position of image:- Between F and C
Nature of image:- Real and inverted
Size of image:- Diminished
3.Position of object:- At C
Position of image:- At C
Nature of image:- Real and inverted
Size of image:- same size
4.Position of object:- Between C and F
Position of image:- Beyond C
Nature of image:- Real and inverted
Size of image:- Enlarged
5.Position of object:- At F
Position of image:- At infinity
Nature of image:- Real and inverted
Size of image:- Highly enlarged
6.Position of object:- Between P and F
Position of image:- Behind the mirror
Nature of image:- Virtual and Erect
Size of image:- Enlarged
Uses of concave mirror:-
- Commonly used in torches , search lights and vehicle headlights to get powerful parallel beam of light .
- Used as shaving mirrors to see large image of the face.
- Dentists use concave mirror to see large images of the teeth of patients.
- Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.
Ray diagrams of images formed by convex mirror:-
1. Position of object:- at infinity
Position of image:- At F
Nature of image :- Virtual and Erect
Size of image :- Highly diminished , point size
2.Position of object:-Between pole and infinity
Position of image:-Between P and F
Nature of image :-Virtual and erect
Size of image:- Diminished
Note :- A full length image of tall building / tree can be seen in a small convex mirror.
Uses of convex mirror:-
- Used as rear view mirrors in vehicle because:-
- Always give an erect though diminished image.
- Have a wider field of view as they are curved outward.
- Used in shoos as security mirror
Sign convention for reflection by spherical mirror:-
- The object is placed to the left of the mirror.
- All distances parallel to the principal Axis are measured from the pole of the mirror.
- All the distances measured to the right of the origin are taken as positive.
- All the distances measured to the left of the origin are taken as negative.
- Distance measured perpendicular to and above the principal Axis are taken as positive.
- Distances measured perpendicular to and below the principal axis are taken as negative.
Note:- object distance= u is always negative
Focal length of concave mirror is negative
Focal length of convex mirror is positive.
Mirror formula:- 1/v + 1/u = 1/f
Where v= image distance from pole
u= object distance from pole
f = focal length
Magnification of spherical mirrors:-
Definition:- It is the ratio of the height of image to the height of object
m=hi/ho where hi= height of image
ho = height of object
Also m= -v/u
If m is negative, image is real
If m is positive, image is virtual
If hi= ho , then m= 1 , i.e image size is equal to object size
If hi>ho , then m> 1, i.e image is enlarged
If hi<ho , them m<1 , i.e image is diminished
Magnification of plane mirror is always +1
If m is positive and less than 1, it is a convex mirror.
If m is positive and more than 1 , it is a comcave mirror.
If m is negative , it is concave mirror.
Assignment:-
Question 1
Find the focal length of a convex mirror whose radius of curvature is 32cm.
Ans:- focal length = 16cm
Question 2
An object is placed at a distance of 10 cm from a convex mirror of focal length 15cm . Find the position and nature of image.
Ans:- v= 6cm nature = virtual and erect
Question 3:-
An object 5 cm in length is placed at a distance of 20 cm in front of convex mirror of radius of curvature 30cm . Find.the position of image , it's nature and size.
Answer :- v = 8.57 cm
h'= 2.1 cm
Nature = virtual and erect
Question 4:-
An object of size 7cm is placed at 27cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed so that a sharp focussed image can be obtained? Find size and nature of image.
Ans:-v= -54-m
h' = -14cm
Nature = real and inverted
Question 5:-
Name the focal length of lens of power -2.0D
Ans:- f = -50cm
Question 6:-
An object 4cm.in size is placed at a distance of 25cm from concave mirror of focal length 15cm. Find the position, nqtuna and height of image.
Ans:- v= -37.5cm
h'= -6--
Nature :- real and inverted
Question 7:-
An arrow 2.5cm high is placed at a distance of 25cm from a diverging mirror of focal length 20 cm. Find nature, position and size of image formed.
Ans:- v= 11.1 cm
h' = 1.11 cm
Nature = virtual and erect
Question 8:-
An erect image 3times the size of object is obtained with comcave mirror of radius of curvature 36 cm. What is the position of object?
Ans:- u= -12cm
Question 9
An object is placed in front of a concave mirror of focal length 20cm. The image formed is 3times the size of object. Calculate two possible distances of the object from mirror?
Ans:- hint :- take m= +3 and m=-3
u1= -40/3cm
U2:- -80/3cm
Question 10
The image formed by a concco mirror if focal length 30cm is a quarter of object. What is the distance of object from mirror?
Ans:- u= -90cm
Part 2
Refraction of light
Introduction:-
- Bending of light when it goes from one medium to another medium is called refraction of light.
- Optical instruments like camera, microscope and telescope work on refraction of light through glass lenses.
- Causes of refraction:- change in speed of light on going from one medium to another.
- Greater the difference in speed of light in two media, greater will be the amount of refraction (or bending) of light.
Some examples of refraction:-
- The bottom of swimming pool appears high.
- Lemons placed in a glass tumbler appear bigger.
- Letters of a book appear to be raised when seen through a glass slab.
- Pencil partially immersed in water appears to be bent at the interface of water and air.
Refraction through a rectangular glass slab:-
- Consider ABCD is a rectangular glass slab.
- When a ray of light (AO) passes into air, strike the glass slab at point O.
- A'O is incident ray.
- After striking it passes through glass slab along OO' .
- Ray OO' is called refracted ray.
- Since air is rarer medium and glass is a denser medium, the refracted ray move towards the normal.
- Now OO' act as a incident ray.
- After striking the surface CD it refract along O'B'
- Since glass is denser medium and air is rarer. So refracted ray move away from the normal.
- Overall we can say that A'O is incident ray, OO' is refracted ray and O'B' is emergent ray.
Note:- in refraction , angle of incidence is usually not equal to angle of refraction.
The perpendicular distance between original path of incident ray and emergent ray coming out of glass slab is called lateral displacement and emergent ray of light.
Whenever a ray of light goes from rarer to denser medium, it bends towards normal .
In this case , angle of incidence> angle of refraction.
Whenever a ray of light goes from denser to rarer medium, it bends away from the normal.
In this case , angle of incidence < angle of refraction.
Optical rarer medium:-
- Also called rarer medium
- Speed of light is high
- Refractive index is less
Optical denser medium:-
- Also called denser medium
- Speed of light is low
- Refractive index is more
- Note :- both these terms are relative terms
Laws of Refraction:-
- The incident ray , the refractive rat and the normal at the point of incident, all lie in the same plane.
- The ration of sign of angle of incidence to the sine of angle of refraction is constant for a given pair of media.
- This constant value is called refractive index of second medium w.r.t. first.
Refractive index :-
- Ratio of speed of light in two media.
- Refractive index of medium 2 w.r.t. medium 1 is the ratio of speed of light in medium 1 and speed of light In medium 2.
- Refractive index of medium 1 w.r.t medium 2 is the ratio of speed of light in medium 2 and speed of light in medium 1.
Absolute refractive index :-
- If the medium 1 is air/ vaccum , then refractive index of medium 2 is considered w.r.t vaccum.
- This is called absolute refractive index of medium.
- Represented by eta 2
- Simply called refractive index of medium.
Refraction of spherical lenses:-
- The transparent material (glass) bounded by two surfaces, of which one or both surfaces are spherical, forms a lens or spherical lens.
Types - convex lens and concave lens.
Convex lens / converging lens:-
Thicker at the middle ; thinner at the edges.
Concave lens/diverging lens :-
Thinner at the middle and thicker at the edges.
Terminology:-
Centre of curvature:-
- A spherical lens has. 2 spherical surfaces.
- Each surface forms a part of sphere.
- Centre of these spheres are called centre of curvature.
- Represented by C1 and C2.
Principal axis:- The imaginary line passing through the centres of curvature of a Lens is called principal Axis
Optical centre:-
- Central point of a lens.
- Represented by letter O
Aperture :-
- The effective diameter of circular outline of a spherical lens.
Principal Focus:-
- When a beam of light parallel to the principal Axis fall on a spherical lens, they converge at a point or appear to diverge from a point. This point on principal Axis is called principal focus of lens.
- Denoted by F1 and F2.
Focal length:-
- The distance of the principal focus from the optical centre is called it's focal length.
- Represented by letter f
Why convex lens is called "converging lens"?
- Because when a beam of light coming parallel to principal Axis passed into the convex lens, it converge at a point called principal focus.
- That's why it is called converging lens.
Why concave lens is called diverging lens?
- When a beam of light falling parallel to principal Axis, after refraction, it gets diverge. That's why it is called diverging lens.
- Rules for image formation in lenses using ray diagrams:-
Rule 1:-
When a ray of light, falling parallel to principal Axis, after refraction it converge /passes through to focus on other side , in case of convex lens and appears to diverge from principal focus located on same side of lens
Rule 2
A ray of light passing through a principal focus, after refraction from a convex lens will emerge parallel to principal Axis.
A ray of light appearing to meet at principal focus of a concave lens after refraction, will emerge parallel to principal axis.
Rule 3:- A ray of light passing through the optical centre of a lens will emerge without any deviation.
Ray diagrams of images formed by a convex lens:-
1. Position of object:- at infinity
Position of image:- at F2
Size of image:-highly Diminished or point sized
Nature of image:- Real and inverted
2.Position of object:- beyond 2F1
Position of image:- between F2 and 2F2
Size of image:- diminished
Nature of image:- Real and inverted
3.Position of object:- At 2F1
Position of image:- At 2F2
Size of image:- same size
Nature of image:- real and inverted
4.Position of object:- between F1 and 2F1
Position of image:- beyond 2F2
Size of image:- enlarged
Nature of image:- Real and inverted
5.Position of object:- at F1
Position of image:- at infinity
Size of image:- highly enlarged
Nature of image:-real and inverted
6.Position of object:- between O and F1
Position of image:- on the same side of lens as object
Size of image:- enlarged
Nature of image:- virtual and erect
Ray diagrams of image formed by a concave lens:-
1.Position of object:- at infinity
Position of image:- at focus F1
Size of image:- highly diminished and point sized
Nature of image:- virtual and erect
2.Position of object:- between infinity and optical centre
Position of image:- between F1 and O
Size of image:- diminished
Nature of image:- virtual and erect
Sign convention for spherical lens:-
- Similar to the one used for spherical mirror except that measurements are taken from optical centre of lens.
- Focal length of convex lens = positive
- Focal length of concave lens = negative
Lens formula:-
- 1/f= 1/v - 1/u
- Where f = focal length
- v = image distance
- u = object distance.
Magnification :-
m = hi/ho = v/u
Power of a lens:-
- It is defined as the reciprocal of focal length in meter.
- P = 1/f = 1/v - 1/u
- The degree of convergence or divergence of light rays is expressed in terms of power.
- SI unit is dioptre (D)
- So 1 dioptre is the Power of lens whose focal length is 1 metre.
- Power of convex lens = positive
- Power of concave lens = negative
- Power of lens combination =
- P = P1 + P2 + P3+....+ Pn
Numerical :-
1. Light enter from air into glass plate having refractive index 1.50 . What is the speed of light in glass?
Ans:- 2x 10^8 m/s
2. If refractive index of water for light going from air to water is 1.33, what will be the refractive index for light going from water to air?
Ans:- 0.75
3. The refractive index of kerosene, turpentine and water are 1.44, 1.47 and 1.33 respectively.. in which of these material does light travel fastest?
Ans:- water
4. A convex lens of focal length 10 cm is placed at a distance of 12 cm from a wall. How far from the lens should a. Object be placed so as to form it's real image on wall?
Ans:-u= -60cm
5. If an object of 7 cm height is placed at a distance of 12 cm from a convex lens of focal length 8cm , find the position, nature and height of image.
Ans:- v = 24cm, nature = real and inverted , h'= -14 cm
6. An object is placed at a distance of 50cm from concave lens of focal length 20cm . Find the nature and position of image.
Ans:- v= -14.3cm and nature = virtual and erect
7. Find power of a concave lens of focal length 2m.
Ans:- P= -0.5D
8. A convex lens forms a real and inverted image of a needle at a distance of 50cm from the lens. If the image is of same size as the needle, where is the needle placed in front of lens ? Also find power of lens.
Ans:- P= 4.0D
Position of object= at 2F2
9. Two thin lenses of power 3.5D and -2.5D are placed in contact. Find the power and focal length of lens combination.
Ans :- P= 1D
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