01
DEFINITION
Reflection
Reflection: Bouncing back of a light ray after hitting a surface.
Incident ray: The light ray which strikes the surface.
Reflected ray: The light ray which returns from the surface after reflection.
Normal: An imaginary line perpendicular to the surface passing from the point of contact.
Angle of incidenceii: Angle between the incident ray and the normal
Angle of reflection rr: Angle between the reflected ray and the normal.
Incident ray: The light ray which strikes the surface.
Reflected ray: The light ray which returns from the surface after reflection.
Normal: An imaginary line perpendicular to the surface passing from the point of contact.
Angle of incidenceii: Angle between the incident ray and the normal
Angle of reflection rr: Angle between the reflected ray and the normal.
02
RESULT
Concave mirror v/s convex mirror
| Concave mirror | Convex Mirror |
| Made by silvering the outer surface of a part of the hollow glass sphere. | Made by silvering the inner surface of a part of the hollow glass sphere. |
| Converging in nature. | Diverging in nature. |
| Image may be real or virtual depending on the position of the object. | Image is virtual. |
| Image may be diminished, same size or magnified. | Image is diminished. |
| The examples of concave mirrors are the mirrors used in automobile head lights, reflecting telescopes, torch lights, etc. | The examples of convex mirrors are the mirrors used as rear side mirrors of vehicles, optical instruments, calling bell, etc. |
03
DEFINITION
Focal length
Focus is defined as the point through which the reflected light rays pass (or appear to pass) when incident light rays are parallel to the principal axis. It is located at the midpoint of pole and centre of curvature. The distance between the pole and the focus of the mirror is called the focal length of the mirror.
Hence, f=R2f=R2
Note: Focal length of the mirror is a measure of power of the mirror.
Hence, f=R2f=R2
Note: Focal length of the mirror is a measure of power of the mirror.
04
FORMULA
Prove that focal length is half of radius of curvature in spherical mirrors
Consider a Concave mirror shown in the figure above.
A ray of light AB traveling parallel to the principal axis PC is incident on a concave mirror at B. After reflection, it goes through the focus F. P is the pole of the mirror. C is the center of curvature.The distance PF = focal length f. The distance PC = radius of curvature R of the mirror. BC is the normal to the mirror at the point of incidence B.
ABC = CBF (Law of reflection, i=r)
ABC = BCF (alternate angles)
BCF = CBF
FBC is an isosceles triangle. Hence, sides BF = FC
For a small aperture of the mirror, the point B is very close to the point P, BF = PF
PF = FC = 1/2 PC
f= 1/2 R
In a similar way, we can also prove this for convex mirror.
A ray of light AB traveling parallel to the principal axis PC is incident on a concave mirror at B. After reflection, it goes through the focus F. P is the pole of the mirror. C is the center of curvature.The distance PF = focal length f. The distance PC = radius of curvature R of the mirror. BC is the normal to the mirror at the point of incidence B.
ABC = CBF (Law of reflection, i=r)
ABC = BCF (alternate angles)
BCF = CBF
FBC is an isosceles triangle. Hence, sides BF = FC
For a small aperture of the mirror, the point B is very close to the point P, BF = PF
PF = FC = 1/2 PC
f= 1/2 R
In a similar way, we can also prove this for convex mirror.
05
DEFINITION
Erect and inverted image
An erect image, in optics, is one that appears right-side up. It is an image in which directions are the same as those in the object, in contrast to an inverted image.
06
DEFINITION
Terms related to spherical mirrors
- Centre of curvature (C): Centre of the sphere of which the mirror is a part.
- Radius of curvature (R): Radius of the sphere of which the mirror is a part.
- Pole (P/O): Geometric centre of the spherical surface of the mirror.
- Principal axis: Straight line joining the pole of the mirror to its centre of curvature.
07
DEFINITION
Focus, Focal length and focal plane of spherical mirrors
The plane through the focus perpendicular to the axis of a mirror or lens is called focal plane.
08
DEFINITION
Define focus, focal length and focal plane of spherical mirrors
Focus
Definition:
For a concave mirror. The rays traveling parallel to the principal axis of a mirror after reflection pass through (converge at) a point F This point F is known as the principal focus of the concave mirror. It is a real point in front of a mirror.
For a convex mirror. The rays traveling parallel to the principal axis of a mirror after reflection appear to diverge from a point F on the principal axis. This point F is known as the principal focus of the convex mirror. It is a virtual point, i.e., behind the mirror.
Focal length
Definition:
The focal length (f) is the distance between the lens and the focal point.Focal Plane:
Definition:
A vertical plane passing through the principal focus and which is perpendicular to the principal axis is called focal plane.
Definition:
For a concave mirror. The rays traveling parallel to the principal axis of a mirror after reflection pass through (converge at) a point F This point F is known as the principal focus of the concave mirror. It is a real point in front of a mirror.
For a convex mirror. The rays traveling parallel to the principal axis of a mirror after reflection appear to diverge from a point F on the principal axis. This point F is known as the principal focus of the convex mirror. It is a virtual point, i.e., behind the mirror.
Focal length
Definition:
The focal length (f) is the distance between the lens and the focal point.Focal Plane:
Definition:
A vertical plane passing through the principal focus and which is perpendicular to the principal axis is called focal plane.
09
DEFINITION
Principal focus and focal plane
A principal focus or focal point is a special focus:
- For a lens, or a spherical or parabolic mirror, it is a point onto which collimated light parallel to the axis is focused. Since light can pass through a lens in either direction, a lens has two focal points one on each side.
- Elliptical mirrors have two focal points: light that passes through one of these before striking the mirror is reflected such that it passes through the other.
- The focus of a hyperbolic mirror is either of two points which have the property that light from one is reflected as if it came from the other.
The plane perpendicular to the axis of a mirror containing the principal focus is called the focal plane.
10
DEFINITION
Virtual and Real images
| Real Image | Virtual Image |
| Real image can be seen on the screen. | Virtual images cannot be formed on the screen. |
| It is always inverted | It is always erect. |
| It is formed when ray of light after reflection.refraction meet at some point | It is formed when ray of light appear to meet at a point. |
| It is formed due to actual intersection of light ray. | It is formed due to imaginary intersection of light ray. |
11
DEFINITION
Real and virtual image
Real image is formed by the actual intersection of light rays. It can be obtained on a screen. Hence, projectors form real images.
Virtual image is formed when the light rays appear to be originating from a point but does not actually meet. It can be seen by human eyes. Hence, rear-view mirrors form virtual images.
Virtual image is formed when the light rays appear to be originating from a point but does not actually meet. It can be seen by human eyes. Hence, rear-view mirrors form virtual images.
12
SHORTCUT
Difference between real and virtual images formed by spherical mirrors
- A real image is defined as one that is formed when rays of light are directed in a fixed point. A real image can be projected or seen on a screen. The best example of a real image is the one formed on a cinema screen.
- A virtual image is defined as the opposite of a real image, therefore an image that cannot be obtained on a screen is referred to as a virtual image. The explanation for this is the fact that the rays of light that form a virtual image never converge therefore a virtual image can never be projected onto a screen. The best example of a virtual image is your reflection in the mirror.
- Real images are produced by intersecting rays while virtual images are produced by diverging rays.
- Real images can be projected on a screen while virtual ones cannot.
- Real images are formed by two opposite lens, concave and convex.
- Virtual images are always upright while real images are always inverted.
13
EXAMPLE
Laws of reflection
In the diagram, the ray of light approaching the mirror is known as the incident ray. The ray of light that leaves the mirror is known as the reflected ray. At the point of incidence where the ray strikes the mirror, a line can be drawn perpendicular to the surface of the mirror. This line is known as a normal line.
The normal line divides the angle between the incident ray and the reflected ray into two equal angles. The angle between the incident ray and the normal is known as the angle of incidence. The angle between the reflected ray and the normal is known as the angle of reflection. The laws of reflection are as follows:
- The incident ray, the reflected ray and the normal to the reflection surface at the point of the incidence lie in the same plane.
- The angle which the incident ray makes with the normal is equal to the angle which the reflected ray makes to the same normal.
- The reflected ray and the incident ray are on the opposite sides of the normal.
14
DEFINITION
Image Formation from Spherical Reflecting Surfaces
The curved shining surface of a spoon acts as a mirror. The inner surface of a spoon acts like a concave mirror, while its outer surface acts like a convex mirror.Hence the inner surface of spoon shows inverted image and outer shows erect.
15
DIAGRAM
Reflection of rays from a spherical mirror
Rays incident on a spherical mirror exhibits the following behaviour:
- Light ray passing through (or directed towards) the center of curvature retraces its path after reflection.
- Light ray parallel to the principal axis passes through (or appears to diverge from) focus after reflection.
- Light ray passing through (or directed towards) focus is reflected as a ray parallel to the principal axis.
- Light ray incident on the pole of the mirror is reflected at an angle of reflection (with principal axis) equal to the angle of incidence (with principal axis).
16
DIAGRAM
Images formed by concave mirrors for object placed at different distances
A concave mirror curves inwards. When parallel rays of light strike the mirror, they are reflected so that they converge to a point. For this reason a concave mirror is also known as a converging mirror. This converging point is the focus of the concave mirror.
17
DIAGRAM
Images formed by convex mirrors for object placed at different distances
A convex mirror bulges outwards. When parallel rays of light strike the mirror, they are reflected so that they spread out or diverge. For this reason a convex mirror is also known as a diverging mirror. If these reflected rays are extended behind the mirror by dotted lines, they are seen to meet at a point. This point is the focus of the convex mirror. It forms small, upright, virtual images.
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