Revision: Optics >> Ray Optics and Optical Instruments Physics Science (English Medium) Class 12 CBSE

A branch of optics that describes light propagation in terms of rays is called ray optics.

For a spherical mirror, the normal at the point of incidence is along the radius, that is, the line joining the centre of curvature of the mirror to the point of incidence, called the normal.

The geometric centre of a spherical mirror is called its pole.

The line joining the pole and the centre of curvature of the spherical mirror is called the principal axis.

The distance between the Principal Focus F and the Pole P of the mirror is called the Focal Length, denoted by f.

f = \[\overline {PF}\]

The plane perpendicular to the principal axis passing through the principal focus F is called the Focal Plane of the mirror.

The point F on the principal axis where a parallel paraxial beam of light converges (or appears to diverge from) after reflection is called the Principal Focus of the mirror.

An image formed when reflected rays do not actually meet, but appear to diverge from a point. A virtual image cannot be obtained on a screen and is located behind the mirror.

An image formed when reflected rays actually converge at a point. A real image can be obtained on a screen and is located in front of the mirror.

Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is known as the principal focus of the concave mirror.

1. Incident ray: The ray of light which falls on the mirror surface is called the incident ray.
2. Point of incidence: The point at which the incident ray falls on the mirror is called the point of incidence.
3. Normal: The normal is a line at right angles to the mirror surface at the point of incidence.
4. Reflected ray: The ray of light which is sent back by the mirror is called the reflected ray.
5. Angle of incidence: The angle of incidence is the angle made by the incident ray with the normal at the point of incidence.
6. Angle of reflection: The angle of reflection is the angle made by the reflected ray with the normal at the point of incidence.

The change in the direction of the path of light when it passes from one transparent medium to another transparent medium is called refraction. The refraction of light is essentially a surface phenomenon.

or

When light passes from one transparent medium to another, its speed and direction change. This is called refraction.

When travelling obliquely from one medium to another, the direction of propagation of light in the second medium changes. This phenomenon is known as refraction of light.

OR

Light changes its direction when going from one transparent medium to another transparent medium. This is called the refraction of light.

OR

The bending of the light ray from its path in passing from one medium to the other medium is called 'refraction' of light.

OR

When a ray of light impinges on a polished, smooth, shiny surface, the rebounding of light within the same medium is called reflection of light.

A normal is an imaginary line drawn perpendicular to the boundary at the point of incidence.

The ray that enters the second medium after crossing the boundary is called the refracted ray.

Refracted light is the part of light enters into the other medium and travels in a straight path but in a direction different from its initial direction and is called the refracted light.

Total internal reflection is the complete reflection of light back into an optically denser medium when light travels from a denser medium to a rarer medium and the angle of incidence exceeds the critical angle.

When a ray of light propagates from a denser medium to a rarer medium, the angle of incidence for which the angle of refraction is 90° is called the critical angle.

The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90 degrees.

An optical fibre is a thin, transparent fibre of glass or plastic that transmits light signals using repeated total internal reflection.

A mirage is an optical illusion seen on hot roads or in deserts where distant objects appear reflected from water-like surfaces.

When rays of light parallel to the principal axis of a mirror are incident on it, the rays after reflection either converge at a point or appear to diverge from a point. The distance of that point from the pole of the mirror is known as the focal length of the mirror.

The point near the centre of a thin lens through which a ray of light passes without appreciable deviation is called the optical centre.

A transparent refracting medium bounded by two surfaces, of which at least one is spherical, is called a lens.

The straight line passing through the optical centre and the centres of curvature of the lens surfaces is called the principal axis.

The point on the principal axis where rays parallel to the principal axis actually meet after refraction, or appear to diverge after refraction, is called the principal focus.

The distance between the optical centre and the principal focus is called the focal length.

The ratio of the height of the image to the height of the object is called magnification.

The deviation of the incident light rays produced by a lens on refraction through it, is a measure of its power.

or

The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P.

OR

The power (P) of a thin lens is equal to the reciprocal of its focal length (f) measured in metres.

Power of a lens is defined as the ability of a lens to bend the rays of light. It is given by the reciprocal of focal length in metre.

The power of a lens is a measure of the deviation produced by it in the path of rays refracted through it.

The SI unit of power of a lens is the dioptre.
One dioptre is the power of a lens whose focal length is 1 metre.

1D = 1m⁻¹

The focal length of a single lens that produces the same optical effect as the given combination of lenses kept in contact.

For a normal, unaided human eye, D = 25 cm. If an object is brought closer than this, we cannot see it clearly. The minimum distance from the eye at which an object can be seen clearly is called the least distance of distinct vision.

OR

Due to the limitation of focusing the eye lens, it is not possible to take an object closer than a certain distance. This distance is called the least distance of distinct vision.

Angular magnification or magnifying power of an optical instrument is defined as the ratio of the visual angle made by the image formed by that optical instrument (β) to the visual angle subtended by the object when kept at the least distance of distinct vision (α).

Angular magnification or magnifying power of an optical instrument is defined as the ratio of the visual angle made by the image formed by that optical instrument (β) to the visual angle subtended by the object when kept at the least distance of distinct vision (α).

A simple magnifier or microscope is a converging lens of small focal length.

An optical instrument that uses objective and eye piece lenses to magnify distant terrestrial or celestial objects is called a telescope.

The resolving power of an astronomical telescope is defined as the reciprocal of the smallest angular separation between two point objects whose images can just be resolved by the telescope.

R.P = `(1.22 lambda)/D`

Resolving power is the ability of the telescope to distinguish clearly between two points whose angular separation is less than the smallest angle that the observer’s eye can resolve.

\[\frac {i}{v}\] + \[\frac {1}{u}\] = \[\frac {1}{f}\]

where:

• v = image distance (measured from the pole)
• u = object distance (measured from the pole)
• f = focal length of the mirror

Relation between focal length and radius of curvature: f = \[\frac {R}{2}\]

For light travelling from medium 1 to medium 2, where medium 1 is denser than medium 2:

For refraction at a spherical surface, the relation is:

\[\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}\]

\[m=\frac{h_i}{h_o}=\frac{v}{u}\]

Where:

• m = magnification.
• h_i = height of image.
• h_o​ = height of object.
• v = image distance.
• u = object distance.

\[\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\]

Where:

• u = object distance.
• v = image distance.
• f = focal length of the lens.

\[\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\]

Where:

• f = focal length of the lens.
• μ = refractive index of the material of the lens with respect to air.
• R₁​ = radius of curvature of the first surface.
• R₂​ = radius of curvature of the second surface.

Power of lens (in D) = \[\frac{1}{\text{focal length (in metre)}}\]

or

P = \[\frac {1}{f}\]

or

P = \[\frac {1}{f (m)}\]

Power of a Lens in a Medium:

P = (n₂ - n₁)\[\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)\] = \[\frac {n_1}{f}\]

\[\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}\]

For more than two thin lenses in contact:

When the image is formed at infinity, the total magnification is:

m = \[m_om_e=\left(\frac{L}{f_o}\right)\left(\frac{D}{f_e}\right)\]

When the final image is at near point: \[m_e=\left(1+\frac{D}{f_e}\right)\]

When final image is at infinity: \[m_e=\left(\frac{D}{f_e}\right)\]

The linear magnification due to the objective is:

1. \[\mathrm{M_{D.D.V}=\frac{f_{o}}{f_{e}}\left(1+\frac{f_{e}}{D}\right)}\]
2. M = \[\frac{\mathrm{f}_{0}}{\mathrm{f}_{0}}\]

• The angle of reflection is equal to the angle of incidence.
• The angle of reflection is the angle between the reflected ray and the normal to the reflecting surface or mirror.
• The angle of incidence is the angle between the incident ray and the normal.
• The incident ray, reflected ray, and the normal to the reflecting surface at the point of incidence lie in the same plane.

Important: These laws are valid at each point on any reflecting surface, whether plane or curved.

The laws of refraction are fundamental for board examinations and objective tests.

First law

The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.

Second law

For a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction remains constant.

\[\frac {\text {sin i}}{\text {sin r}}\] = constant

This constant is called the refractive index of the second medium with respect to the first medium.

• The laws of reflection apply to both plane and curved reflecting surfaces.
• In spherical mirrors, the normal is taken at the point of incidence.
• The normal is along the radius joining the centre of curvature to the point of incidence.
• The geometric centre of a spherical mirror is called the pole.
• The line joining the pole and the centre of curvature is the principal axis.