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• Important definitions:
• Light : Form of energy that enables us to see objects.
• Ray of light / Light ray : Straight line representing the path of light.
• Normal: Line drawn perpendicular to surface on which light falls.
• Incident ray : Ray of light falling on an object.
• Reflected ray : Ray of light that get reflected from an object.
• Angle of incidence : Angle between incident ray and normal.
• Angle of reflection : Angle between reflected ray and normal.
• Laws of Reflection of Light :

1. Incident ray, Reflected ray and normal lie in same plane.
2. Angle of incidence is equal to angle of  reflection. θi = θr

• Image formed by plane mirror :
• Image formed by plane mirror is virtual, erect and laterally inverted.
• Size of image = Size of object.
• Object Distance  = Image Distance.
• Spherical Mirror :
• Reflecting surface of spherical mirror are curved (inward or outward).
• Concave mirrors: Reflecting surface are curved inward/ towards centre.
• Convex mirrors: Reflecting surface are curved outward/ away from centre.
• Important terms in spherical mirror:
1. Pole (P) : Center of spherical mirror is called pole.
2. Center of Curvature (C) : If a curved surface is a part of sphere, then the centre of sphere is called centre of curvature.
3. Radius of curvature (R) : Distance of pole from centre of curvature. Radius of curvature is at equal distance from any point on the mirror.  
4. Principal axis : A straight line passing through center of curvature and pole.
5. Principal focus(F) : Rays falling on mirror converges on common point called principal focus.
6. Focal length (f) : Distance between pole P and focus F.
7. Aperture : Diameter of reflecting surface of mirror.  
8. Object distance (u) : Distance of  object from the pole.
9. Image distance (v) : Distance of object from the pole.
• Image formation using ray diagram

Incident ray	Ray Diagram	Reflected Ray
Parallel to principal axis		Passes through focus
Passes through the focus		Parallel to principal axis
Passes through center of curvature		Reflects back along same path
Passes through pole P		Reflected ray makes same angle to angle of incidence (Follows law of reflection)

 

• Image formation by spherical mirror : Concave mirror

Position of Object	Parameters of Image formation	Ray Diagram
At infinity	At focus, point sized, real and inverted
Just beyond C	Between center of curvature and focus, diminished, real and inverted
At C	Same size, real and inverted. Image forms at C
Placed between F and C	Beyond C,  enlarged, real and inverted
At  F	At infinity, enlarged, real and inverted
Object between P and F	Magnified, virtual and erect image

• Uses of concave mirror :
• Used in torches, searchlights, vehicle headlights to get strong parallel beam of light.
• Dentists use them to view large image of teeth’s of the patients.
• Large concave mirrors are used to concentrate sunlight, to get heat in solar furnaces.
• Image formation by spherical mirror : Convex mirror

Position of the Object	Image formed	Ray diagram
At infinity	At focus,  point sized, virtual and erect image
Between infinity and pole P	Between P and F, short, virtual and erect

 

• Uses of convex mirrors :

 

• Used as Rear-view mirrors in vehicles.
• In various places like corners in hospitals, offices to see the people and objects at the corner in order to avoid accident.
• New cartesian sign convention :
• Object must be placed to the left of the mirror.
• Distances parallel to principal axis is measured from pole of mirror.
• Distances measured to right of origin (plus x axis) are taken as positive.
• Distances measured to the left of the origin (minus x axis) are taken as negative.
• Distances measured above the principal axis ( plus y axis) are taken as positive.
• Distances measured below the principal axis (minus y axis) are taken as negative.
• Mirror Formula : 1/u + 1/v  = 1/f     
• Relation between Radius of curvature and focal length : R = 2f  
• Magnification (m) :

Magnification (m)	Image formed
Positive (+m)	Virtual and erect
Negative (- m)	Real and inverted

• Refraction of  light :  [Refer the video to understand in detail]
• “Phenomenon of change in direction of ray of light while passing from one medium to another.” E.g. Refraction through glass slab. Refraction occurs because in rare medium light travels faster speed(e.g. air = 3108m/s), while in denser medium it travels with slower speed (e.g. diamond = 1.24108 m/s).

 

• Laws of refraction: [Refer the video to understand in detail]

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.

 

• Snell’s Law : The ratio of sine of angle of incidence (i) to the sine of angle of refraction(r) is a constant, for the light of a given colour and for the given pair of media.

 

Sin i / Sin r    =    Constant

• Refractive index (η) : It is change in direction of light in that medium. Constant obtained from snell’s law is refractive index.
• Refractive index of one medium with respect to another can be given by:

• Absolute Refractive index (ηm) :

Refractive index of medium 1 and medium 2	Speed of light	Ray of light
η1 < η2	Decreases	Bends towards normal
η1 > η2	Increases	Bends away from normal

• Difference between Reflection and Refraction

Reflection	Refraction
Light rays are sent back by an object	Light rays bent when passed through an object
Medium of incident ray and reflected ray is same	Medium of incident ray and refracted ray is different
Angle of incidence is equal to Angle of reflection	Angle of incidence is not equal to Angle of refraction
Reflection occurs in mirrors	Refraction occurs in lenses
E.g. Mirrors in cars, household purpose	E.g. concave & convex lenses, glass slab, pencil half immersed in water

 

•  

 

• Lens: Transparent material having one or two curved surfaces.
• Convex lens / Double convex lens / Converging lens : Lens thicker in middle as compared to edges.
• Concave lens / Double concave lens / Diverging lens : Lens thicker at the edges as compared  in middle.
• Image formation by lens :

Incident ray	Convex lens	Concave lens
Parallel to principal axis	Ray converges to focus F2	Ray appear to diverge from focus F1
Passing through focus	Refracts from focus F1, emergent ray is parallel to principal axis	Likely to pass through focus but diverges parallel to principal axis
Passing through optical centre	No change in direction	No change in direction

• Image formation in Convex lens :

Position of object	Ray Diagram	Image formed
Object at infinity		Point sized, real and inverted image at focus F2
Object placed beyond 2F1		Diminished, real and inverted image between F2 and 2F2
Object placed at 2F1		Same sized, real and inverted image forms at  2F2
Object placed between  F1  and 2F1		Enlarged, real and inverted image, forms beyond  2F2
Object placed at F1		Infinitely enlarged, real and inverted image forms at infinity.
Object placed between focus F1 and optical centre O		Enlarged, virtual and erect  image forms on the same side of the object

• Image formation in Concave lens :

Position of Object	Ray diagram	Image formed
Object at infinity		Point sized, virtual and erect image forms at focus F1
Object placed between infinity and optical center O		Diminished Image forms between focus F1 and optical center O

 

• Convex lens v/s Concave lens

Convex lens	Concave lens
Thicker in middle , thinner at edges	Thinner in middle, thicker at edges
Converges rays of light	Diverges rays of light
Image formed can be virtual, real, enlarged or diminished depending on object position	Image formed is virtual and diminished
Focal length is positive	Focal Length is negative
Used  in correction of hypermetropia	Used in correction myopia

 

• Lens formula :  1v–1u=1f
• Magnification of lens (m):

Magnification (m)	Image
Positive (+ m)	Upright
Negative (- m)	Inverted

• Power of lens (P) : Reciprocal of focal length i.e. P= 1/f . Measured in diopter (D). 1 diopter is the power of lens having focal length 1m.
• Significance of power of lens :
• Signifies degree to which a lens converges or diverges light rays falling on it.
• Convex lens : Larger the power of lens, rays converges to large angle. Smaller the power of lens, rays converges to smaller angle.

Concave lens : Larger the power of lens higher is divergence. Smaller the power of lens lesser is the divergence.