CBSE Class 12 Physics Notes Chapter 9 Ray Optics

We can see objects around us because of the light reflected or emitted by them. Nature has given us eyes, which can detect a small region of electromagnetic radiation spectrum, known as visible light. Light travels with great speed in a straight line.

Optics is a branch of physics that deals with the study of nature, production, and propagation of light.

Optics is divided into categories:

• Ray optics or Geometrical optics
• Wave optics or Physical optics

Light is a wave. Although a light wave spreads as it moves away from its source, we can approximate its path as a straight line. Under this approximation, we show light as a ray and the study of light as a ray is called Ray optics or Geometrical optics. CBSE Class 12 Physics Notes for Chapter 9 Ray Optics are given in the article below for easy preparation and understanding of the concepts involved.

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Class 12 Physics Chapter 9 Notes - Ray Optics

Light

• The visible part of the electromagnetic spectrum is called Light.
• Light always travels in a straight line.
• The speed of light in vacuum or air is 3 x 10⁸ m/s.
• The straight line in which the light travels is known as a Ray of Light.
• The bundle of parallel rays of light is called a Beam of Light.

Laws of Reflection

• According to the law of reflection, the angle of incidence (∠i) is equal to the angle of reflection (∠r).
• The incident ray, the reflected ray, and the normal, all lie in the same plane.
• After reflection, the velocity, wavelength, and frequency of the light remain the same.

Laws of reflection

Spherical Mirrors

• Concave Mirror: It is a part of a hollow sphere that converges the rays of light.
• Convex Mirror: It is a part of a hollow sphere that diverges the rays of light.

Spherical Mirrors

Terms Related to Spherical Mirrors

• Pole (P): Mid-point of the mirror.
• Center of Curvature (C): Center of the sphere of which the mirror is a part.
• Radius of Curvature (R): Distance between pole and center of curvature.
• Principal axis: A line passing through pole and center of curvature.
• Focus (F): The image point on the principal axis for an object at infinity.
• Focal length (f): Distance between pole and focus.

Sign Convention

• All distances are measured from the pole.
• Distances measured in the direction of the incident ray are taken as “Positive”.
• Distances measured in the direction opposite of the incident ray are taken as “Negative”.
• Distances above the principal axis are taken as “Positive”.
• Distances below the principal axis are taken as “Negative”.

Sign conventions for spherical mirrors

Image Formation by Concave Mirror

Image Formation by Convex Mirror

Relation Between Focal Length and Radius of Curvature

• Formula:

f = R/2

Where

• f is the focal length
• R is the radius of curvature

• This formula is valid for both concave and convex mirrors
• For a plane mirror, f = ∞ and also R = ∞

Mirror Formula

• The relation between the focal length of a lens, object distance, and image distance is known as the mirror formula.
• Formula:

1/f = 1/u + 1/v

Where

• f is the focal length
• u is the distance of the object
• v is the distance of the image

• This formula is valid for both concave and convex mirrors.

Magnification

• It is the ratio of the height of the image to the height of the object.
• Formula:

m = h’/h

Where

• m is the magnification
• h’ is the height of the image
• h is the height of the object
• It is positive for erect images.
• It is negative for inverted images.

Refraction of Light

• The bending of the ray of light passing from one medium to another medium is called refraction.
• A ray of light bends towards the normal while traveling from a rarer to a denser medium.
• A ray of light bends away from the normal while traveling from a denser to a rarer medium.

Refraction of light

Snell’s Law

• Snell’s law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.
• This constant is known as the Refractive Index.
• Formula:

sin i / sin r = μ

Where

• i is the angle of incidence
• r is the angle of refraction
• μ is the refractive index

Total Internal Reflection (TIR)

• The phenomenon in which a ray of light traveling from a denser to a rarer medium is sent back to the same denser medium is known as Total Internal Reflection.
• Condition for TIR:
• Light travels from denser medium to rarer medium.
• The angle of incidence must be greater than the critical angle.

Total Internal Reflection

Relation Between Refractive Index and Critical Angle

• Formula:

sin C = 1/μ

Where

• C is the critical angle
• μ is the refractive index

Refraction from Spherical Surface

• Refraction Formula:

(μ₂ - μ₁)/R = μ₂/v - μ₁/u

Where

• μ₁ is the refractive index of the medium from which light rays are coming
• μ₂ is the refractive index of the medium in which light rays are entering
• u is the object distance
• v is the image distance
• R is the radius of curvature.

The Lens

• A lens is a transparent medium bounded by two refracting surfaces such that at least one surface is curved.
• Types of Lens:
• Concave Lens: It is also known as a Diverging lens.
• Convex Lens: It is also known as a Converging lens.

Concave and Convex Lenses

Lens Maker’s Formula

• Lens Maker’s Formula:

1/f = (μ - 1) [1/R₁ - 1/R₂]

Where

• f is the focal length of the lens
• μ is the refractive index
• R₁ is the radius of curvature of the first refractive surface
• R₂ is the radius of curvature of the second refractive surface

Lens Maker’s Formula

Lens Formula

• Formula:

1/f = 1/v - 1/u

Where

• f is the focal length of the lens
• u is the distance of the object from the lens
• v is the distance of the image from the lens

Image Formation by Convex Lens

Image Formation by Concave Lens

Magnification of Lens

• Formula:

m = h’/h = v/u

Where

• m is the magnification
• h’ is the height of the image
• h is the height of the object
• v is the image distance
• u is the object distance

Power of a Lens

• The power of a lens is the ability of a lens to converge or diverge rays of light falling on it.
• It is the reciprocal of the focal length of the lens.
• Formula:
• P = 1/f

Where

• P is the power of the lens
• f is the focal length of the lens in meters.

• The SI unit of power of the lens is Dioptre (D).

Prism Formula

• Formula:

μ = sin [(A +\(\delta\) _m)/2] / sin (A/2)

Where

• μ is the refractive index of the prism
• \(\delta\)_m is the angle of minimum deviation.
• A is the prism angle.

Prism

Microscope

• It is an optical instrument used to see very small objects.
• Types: 

• Simple Microscope
• Compound Microscope

Simple Microscope

• It is a convex lens of lesser focal length.
• It is also called a magnifying glass or reading lens.
• Magnification, when the final image is formed at least a distance of distinct vision (D) is

m_D = [1 + D/f]_max

• Magnification, when the final image is formed at infinity is

m_∞ = [D/f]_min

Compound Microscope

• It consists of two converging lenses called objective and eye lens.
• The final image formed is magnified, virtual, and inverted.
• Magnification, when the final image is formed at least a distance of distinct vision (D) is

m_D = - v_o/u_o [1 + D/f_e]

• Magnification, when the final image is formed at infinity is

m_∞ = - v_o/u_o [D/f_e]

Astronomical Telescope

• This type of telescope is used to see heavenly bodies.
• The focal length of the object is greater than the focal length of the eyepiece.
• The final image is virtual, inverted, and small.
• Magnification, when the final image is formed at least a distance of distinct vision (D) is

m_D = - f_o/f_e [1 + f_e/D]

• Magnification, when the final image is formed at infinity is

m_∞ = - f_o/f_o

There are Some important List Of Top Physics Questions On Ray Optics And Optical Instruments Asked In CBSE CLASS XII