0What is a Spherical Mirror?
It is a part of the reflective spherical surface and is spherical in shape. Spherical mirrors consist of a large number of extremely small plane mirrors.
They are of two types:
Concave Mirror: It is a mirror which is silvered on the inward part of the sphere and does not face the incident light. It is a converging mirror where the rays of light converge or meet at a single point.
Convex Mirror: It is a mirror which is silvered on the outward part of the sphere. Here the rays of light do not meet at a particular point after reflection. Therefore, it is said to be a diverging mirror.
Basic Terminologies
Pole: The geometric centre of the reflecting surface of the mirror is said to be the Pole and is denoted by P. It serves as an origin and lies on the surface of the spherical mirror.
Centre of curvature:
The mirror’s reflecting surface forms a part of an imaginary sphere. The sphere’s centre or midpoint of the aperture is called the centre of curvature and is denoted by C. For a concave mirror, C is in front, whereas for a convex mirror, it is behind it.
NOTE: The centre of curvature does not lie on the mirror. It lies outside of the reflecting surface of the spherical mirror.
The radius of curvature
The radius of an imaginary sphere from which the reflecting surface of a spherical mirror is cut is called the radius of curvature and is denoted by R.
Principal axis
A straight line which passes through the pole and the centre of curvature of the spherical mirror is the principal axis. The principal axis is normal or perpendicular to the mirror at the pole.
Focus
The rays which are parallel to the principal axis fall on a concave mirror that meets or intersects at the point on the principal axis. The point is known as the focus of the concave mirror.
The reflected rays appear to come from the point on a principal axis when the rays parallel to the principal axis fall on the convex mirror. This point is termed the principal focus of the convex mirror. It is denoted by F.
The distance between the pole and the focus of a mirror is known as the focal length and is represented by F. .
Aperture
Aperture is the diameter of the reflecting surface of the spherical mirror.
If the aperture is smaller than the radius of curvature(R), we get R= 2f.
It is essential for students to gain a deeper understanding of these terms to understand complex concepts included in the Class 12 Physics Chapter 9 notes.
Image formation by Spherical Mirrors
- The light rays passing through the centre of curvature trace the same path.
- The ray of light which passes parallel to the principal axis after reflection passes through the principal focus.
- The light rays passing through F get reflected back and travel parallel to the principal axis.
- There are two types of images formed: –
- Real images of an object are formed where the reflected rays meet. It is inverted and formed on the same side of the object.
- Virtual images of the object are formed where the reflected rays appear to meet. It is erect and cannot be obtained on the screen as it is formed beyond the spherical mirror.
Sign Conventions
- The pole (P) is considered the origin. The principal axis of the mirror is considered to be the x-axis of the coordinate system.
- The object is always placed on the left-hand side of the mirror. This means that the light will fall on the mirror from the left.
- The distances that are parallel to the principal axis of the spherical mirror are measured from the pole of the mirror.
- The distances measured from the right of the origin are taken as positive, and those to the left of the origin will be taken as negative.
- The distances measured perpendicular to the principal axis, i.e., along + y-axis, will be taken as positive and along – y-axis are taken as negative.
- The heights which are measured upwards for the x-axis are normal to the principal axis of the mirror or lens and are positive, and the heights measured downwards will be negative.
- The radius of curvature (R) and the focal length of a concave mirror is always negative, and for a convex mirror are positive.
The signs and conventions are essential in solving problems included in the Class 12 Physics Chapter 9 notes.
Mirror Formula
For a Concave Mirror
Let u be the distance of the object from the pole known as object distance, v is the distance of the image from the pole known as image distance, and f is the distance of principal focus from the pole, called the focal length.
(1v) + (1u) = (1f) is the mirror equation for concave mirror and
(1f) = (1v) – (-1u) is the mirror equation for convex mirrors.
Students can practice a number of problems included in the Class 12 Physics Chapter 9 notes.
Magnification of a Spherical Mirror:
Linear magnification of a spherical mirror, denoted by m, gives the proximate extent to which the image of the object can be magnified with respect to the object size.
Mathematically,
m= (height of the image h’height of the object h)
Or, m = (h’h)
If magnification is negative, then it implies that the image is real, and if it is positive, then the image is taken to be virtual.
For a concave mirror, m = (-vu) and for a convex mirror, m= -(vu)
REFRACTION OF LIGHT
Light travels in different directions in different media. When the light rays pass obliquely from a rarer medium to the denser medium, the direction of the propagation of light changes.
When a light ray passes from one medium to another, it bends. This is refraction.
This phenomenon takes place due to the change in the velocity of light from one medium to another.
Laws of Refraction (Snell’s law):
The incident light ray, refracted light ray and normal at the incidence point lie in the same plane.
The ratio of sin (i) to sin (r) is constant.
The angle of incidence (i) is described by the incident ray and is normal. Similarly, the angle of refraction (r) is the angle between refracted ray and the normal.
21 = (sin isin r)
Where 21= is the refractive index of the second medium with respect to the first.
NOTE: The refractive index (21) is dependent on the wavelength of light and the characteristic of mediums.
If 21 >1, r<i, this implies that the refracted light ray bends towards the normal. Therefore, the second medium will be optically denser than the first medium.
If 21<1, r>i this implies that the refracted light ray bends away from the normal. Therefore, the second medium will be optically rarer than the first medium.
Refraction through a Rectangular Glass Slab
For a parallel-side slab, refraction occurs at two interfaces, i.e., at the air-glass and glass-air interface. The emergent ray passes in the direction parallel to the incident ray. Therefore, there will be no deviation.
However, there is a lateral shift with respect to the incident ray.
The refractive index of medium 2 with medium 1 is given as 21=21, where 1, 2= refractive index of medium 1 and 2 ,respectively.
To understand the refraction of light thoroughly, students must refer to the Class 12 Physics Chapter 9 notes.
Natural phenomena of Refraction
- Advance Sunrise and Delay in Sunset:
We can see the sun a little before the actual sunrise occurs and a little after the actual sunset. This happens due to the phenomenon of the refraction of light in the atmosphere.
Actual sunrise means the crossing of the horizon by the sun.
The apparent shift of light towards the sun is by approximately half a degree and therefore this results in a corresponding time difference between the actual sunset and apparent sunset by a difference of 2 minutes.
The oval shape of the sun when it sets and rises is also due to the refraction.
- Twinkling
We know that stars have their own light. They appear to be twinkling because as the light reaches our eye, it passes through different layers of the atmosphere.
At one point in time the star appears to be at one position, and in another minute, it is at another position. This means that the object is at two different places at a frequent time interval.
Each concept is well explained in the Class 12 Physics Chapter 9 notes.
TOTAL INTERNAL REFLECTION
When the ray of light travels from the optically denser medium to an optically rarer medium, it gets partly reflected into the first medium and partly refracted into the second. This reflection is known as internal reflection.
In total internal reflection, the refraction of light into the second medium does not take place. This means that the entire incident ray gets reflected.
Conditions for Total Internal Reflection(TIR)
- Light rays must pass from optically denser to an optically rarer medium.
- When a ray of light travels, it moves away from the normal. Refraction takes place at a point r (angle of refraction).
- If the angle of incidence increases, the light ray moves away from normal, and the angle of refraction reduces.
- On further increasing the angle of incidence(i), the angle of refraction becomes equal to 90. If the angle of incidence increases more, then no refraction will occur. In this case, the reflection will take place. This is known as Total Internal Reflection.
The limiting factor will be as follows:
- The angle of incidence for which the angle of refraction is 90 must be smaller than the angle of incidence (i).
- The angle of incidence must be equal to the angle of refraction = 90. This is the Critical angle.
- The angle of incidence (i) has to be greater than the critical angle.
