Reflection of Light:
When a ray of light incident on a reflecting surface of medium, the light will be send back into the same medium is called as reflection of light.
The laws of reflection for any mirror are as given below:
- First law: The incident ray, reflected ray and normal lies in the same plane.
- Second law: The angle of reflection is always equal to the angle of incidence.
- Third law: The incident ray & reflected ray lie on the opposite sides to that of normal.
Spherical Mirrors:
On the basis of the direction of curvature there are two types of spherical mirrors.
- Concave mirrors: A concave mirror is the spherical mirror in which light is reflected from the concave surface or bent in surface.
- Convex mirrors: A convex mirror is a spherical mirror in which light is reflected from the spherical surface which is outward in curvature or bulged outwards.
Now we define some terms in case of spherical mirrors by seeing the following diagram.
- Pole of the spherical mirror:
- Pole of the spherical mirror is the center point on the reflecting surface of spherical mirror.
- It is denoted by P.
- Center of curvature of the spherical mirror:
- The spherical reflecting surface has its own center i.e. center of sphere which is called as center of curvature of spherical mirror.
- It is denoted by C.
- Radius of curvature of spherical mirror:
- Radius of curvature is the radius of spherical reflecting surface forming the spherical mirror.
- It is denoted by R.
- Principal axis of spherical mirror:
- The line joining the distance between the pole and the center of curvature of spherical mirror is called as principal axis of spherical mirror.
- Principal axis is always perpendicular to the spherical mirror at its pole.
- Principal focus or Focal point of the spherical mirror:
- Consider the parallel beam of light is incident on the reflecting surface of a concave mirror as shown in fig.a).
- After reflecting from the concave surface, all these rays meet at a same point on the principal axis. The point at which all the rays meet on the principal axis is called as principal focus or focal point of the concave mirror.
- Similarly, in case of convex mirror, the reflected rays coming from reflecting surface of convex mirror are appears to come from a common point behind the reflecting surface on principal axis as shown in fig. b).
- This common point on principal axis is called as principal focus or focal point of the convex mirror.
- The principal focus or focal point is represented by F.
- Focal length of the spherical mirror:
- The distance between the principal focus and the pole of the mirror is called as the focal length of the spherical mirror.
- It is denoted by f.
Image formation by Spherical mirror and their representations using Ray diagrams:
- a) shows that, when a ray of light parallel to principal axis is incident on concave mirror then it gets reflected by passing through focal point F.
- And in case of convex mirror the same incident rays will appears to diverge from the focal point after reflection as shown in fig.b).
- The ray of light passing through focal point will be reflected parallel to principal axis in case of concave mirror as in figa).
- The ray of light directed towards the focal point in case of convex lens also be reflected as a parallel ray to principal axis as in fig.b).
- A ray of light incident on the reflecting surface of concave mirror passing through the curvature or directed in the direction of center of curvature in case of convex mirror will be reflected back along the same path.
- Because the rays passing through the center of curvature are normal to the reflecting surface of mirror as shown in above fig.a) and b).
- The ray of light incident obliquely to the principal axis in case of concave mirror and convex mirror will be reflected obliquely as shown in above fig.a) and b).
Image formation by a concave mirror for different positions of the object:
Following are the ray diagrams showing image formation by a concave mirror for different positions of the object.
Position of object: At infinity
Position of the image: At the focus
Size of the image: Highly diminished & point size
Nature of image: Real & inverted
Position of object: Beyond C
Position of the image: Between F and C
Size of the image: Diminished
Nature of image: Real & inverted
Position of object: At C
Position of the image: At C
Size of the image: Same size
Nature of image: Real & inverted
Position of object: Between C and F
Position of the image: Beyond C
Size of the image: Enlarged
Nature of image: Real & inverted
Position of object: At F
Position of the image: At infinity
Size of the image: Highly enlarged
Nature of image: Real & inverted
Position of object: Between P & F
Position of the image: Behind the mirror
Size of the image: Enlarged
Nature of image: Virtual & erect
Uses of Convex Mirrors:
- Convex mirrors are mostly used in vehicles to see the vehicles at a distant apart from it.
- The driver can see full image of the vehicle behind it & surrounding area also for safe driving.
Sign conventions for reflection by spherical mirrors:
While designating the sign conventions for reflection by spherical mirrors we have to consider the pole P of the mirror as origin O and the principal axis as the X axis of the Cartesian coordinate system.
The sign conventions for reflection by spherical mirror are as follows:
- All the distances are measured from the pole P of the mirror.
- All the distances measured to the right of pole are taken as positive while the distances measured to the left of pole are taken as negative.
- Distances measured above & normal to principal axis are taken as positive.
- Distances measured below & normal to principal axis are taken as negative.
- If the image is real then image distance is taken as negative.
- If the image is virtual then the image distance is taken as positive.
- Focal length of concave mirror is negative while the focal length of convex mirror is positive.
- The fig. given below explains the sign conventions in case of spherical mirrors
Mirror Formula and Magnification:
Fig. representation of sign conventions in Cartesian coordinate system for spherical mirror
Object distance (u):
- The distance of object from the pole of the spherical mirror is called object distance.
- It is denoted by u.
Image distance (v):
- The distance of image from the pole of spherical mirror is called as image distance.
- It is denoted by v.
- The mirror formula gives the relationship between object distance, image distance & focal length of spherical mirror which is given by,
1/v + 1/u = 1/f
i.e. 1/image distance + 1/ object distance = 1/ focal length
Magnification:
Magnification is the ratio of height of image to the height of object & it is denoted by m.
m = height of the image/ height of the object =h’ /h
Magnification in terms of image distance & object distance is given as
Magnification m = h’/h = -v/u
Magnification gives the relative extent of magnified image with respect to the original object size.
Note: When m is negative, then image is real.
When m is positive, then image is virtual.
Refraction of light:
When light travels from one transparent medium to another transparent medium its direction changes in second medium which is called as refraction of light. The direction of changing the ray depends on the refractive index of the medium & speed of light in that medium. Thus, all these examples explains that light does not travel in straight line in all the media. Its direction of travelling depends on the refractive index of the media.
The laws of refraction concluded are as follows:
- i) The incident ray, refracted ray and normal to the interface separating two media all lie in the same plane.
- ii) The ratio of sine of angle of incidence to the sine of angle of refraction is constant and this constant is called as refractive index of the second medium with respect to first medium.
This law is also called as Snell’s law of refraction& it is valid for 0<i<90.
Then, sini/sinr = constant
i-Angle of incidence
r- Angle of refraction
sini/sinr= Refractive index of second medium with respect to first medium
The Refractive Index:
The refractive index of the medium depends on the speed of light in that medium. The speed of light in vacuum is largest and which is 3* 108 m/s. In air it decreases slowly and more in water and glass.
Then the refractive index of second medium with respect to first is the ratio of speed of light in medium 1 to the speed of light in medium 2.
It is given by, μ21 = speed of light in medium 1/ speed of light in medium 2
= V1/V2
Similarly, the refractive index of medium 1 with respect to medium 2 is given by,
Μ12 = speed of light in medium 2/ speed of light in medium 1 = V2/V1
Absolute Refractive Index:
If the medium 1 is air or vacuum then refractive index of medium 2 with respect to air or vacuum is called as absolute refractive index of the medium and it is denoted by
μm = speed of light in air/ speed of light in medium = c/v
Where c- speed of light in air or vacuum
v- Velocity of light in medium
Image formation in lenses using Ray diagram:
Lenses form the image by refracting light. How they forms the images, what is their nature, all this points are discussed in this topic.
Let us first see, how the refraction of light occurs in lenses:
i)
In case of convex lens, the light ray incident parallel to principal axis after refraction passes through the focus on the other side of lens as in fig.
In case of concave lens, light ray incident parallel to principal axis, after refraction appears to diverge from the principal focus on the same side of lens as in fig.
ii)
In convex lens, the ray of light passing through focus after refraction it appears parallel to the principal axis as in fig.
In convex lens, the ray of light appearing to meet at the focus, after refraction it will emerge parallel to principal axis as in fig.
iii)
In both concave and convex lens, the ray of light passing through optical center of lens, after refraction emerges without any deviation as in fig.
Let us discuss how images are formed, their nature and location in case of convex lens using ray diagrams:
Mindmap Class 10 Science Chapter 10Sign conventions for spherical lens:
- The sign conventions for spherical lenses are similar to the sign conventions for spherical mirror.
- Here all the distances are taken from optical center O.
- The focal length of convex lens is positive and that of concave lens is negative.
Lens formula and Magnification:
The lens formula gives the relation between object distance u, image distance v and the focal length f. It is given by
1/v – 1/u = 1/f
Magnification:
Magnification of lens is the ratio of height of image to the height of object.
It is denoted by m.
Magnification m = height of image/ height of object = h’ / h
Magnification is also given by,
Magnification m = h’ / h = v / u
Power of lens:
- The ability of lens to bend all the rays passing through it is called as power of lens.
- It is denoted by P.
P = 1/ focal length of lens
P = 1/ f = 100/ focal length in cm
- I. unit of power of lens is diopter & denoted by D.
- If f is in meters, then P is in D.
- The power of convex lens is positive & that of concave lens is negative.