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

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.

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.

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.

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

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

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.

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

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

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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.

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).

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.

Principal focus (F): The point on the principal axis of the spherical mirror where the rays of light parallel to the principal axis meet or appear to meet after reflection from the spherical mirror.

The point inside a lens on the principal axis, through which light rays pass without changing their path is called the optical centre of a lens.

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The point on the principal axis of a lens such that a ray of light directed towards it emerges from the lens in the same direction, without deviation.

A lens which is bent inwards in the middle is a concave lens. Such a lens diverges the light rays incident on it, so it is also called a diverging lens.

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This lens is thicker near the centre as compared to the edges. The lens with both surfaces spherical on the inside is called a concave or double concave lens.

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The lenses which are thinner in the middle and thicker at the edges, are called 'concave lenses'.

A lens which bulges out in the middle, is a convex lens. A light beam converges on passing through such a lens, so it is also called a converging lens.

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The lens which has two spherical surfaces which are puffed up outwards is called a convex or double convex lens.

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The lenses which are thicker in the middle and thinner at the edges, are called 'convex lenses'.

Principal focus (F) is the point on the principal axis at which light rays parallel to the principal axis converge after passing through a convex lens.

A lens is a transparent refracting medium bounded by either two spherical surfaces, or one spherical surface and the other surface plane.

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A lens is a transparent medium bound by two surfaces.

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A lens is a transparent medium (such as glass) bounded by two curved surfaces or one curved and one plane surface.

The imaginary line passing through both centres of curvature is called the principal axis of the lens.

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The line joining the centres of curvature of the surfaces of the lens is called the 'principal axis' of the lens.

The distance between the optical centre and principal focus of a lens is called its focal length.

The centres of spheres whose parts form surfaces of the lenses are called centres of curvatures of the lenses.

The radii (R₁ and R₂) of the spheres whose parts form surfaces of the lenses are called the radii of curvature of the lens.

The angular separation between the two extreme colours (violet and red) in the spectrum (which is obtained by passing a beam of white light through a prism) is known as angular dispersion.

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 distance of the principal focus from the pole is called the focal length (f).

The distance of the image from the pole of the mirror is called the image distance (v).

In a spherical mirror, the distance of the object from its pole is called the object distance (u).

An optical instrument used to observe distant objects by producing angular magnification is called a telescope.

The ratio of the sine of the angle of incidence to the sine of the angle of refraction for a given pair of media is called refractive index.

The phenomenon in which a ray of light travelling from a denser to a rarer medium is completely reflected back into the denser medium when the angle of incidence exceeds the critical angle is called total internal reflection.

The change in direction of light when it passes obliquely from one transparent medium to another due to change in speed is called refraction of light.

The phenomenon in which light returns back into the same medium after striking a reflecting surface is called reflection of light.

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

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

Magnification (m) = \[\frac{\text{Height of the image (}h'\text{)}}{\text{Height of the object (}h\text{)}}\] = \[\frac {h'}{h}\]

Magnification in terms of object and image distances:

Magnification (m) = \[\frac {h'}{h}\] = -\[\frac {v}{u}\]

• The laws of reflection describe the behaviour of light when it strikes a reflecting surface.
• The first law states that the incident ray, the reflected ray and the normal drawn at the point of incidence all lie in the same plane.
• The second law states that the angle of reflection is always equal to the angle of incidence.
• These laws are valid for all reflecting surfaces, whether plane or curved. In the case of spherical mirrors, the normal at any point on the surface passes through the centre of curvature.
• The laws are independent of the nature of the reflecting material. Reflection also obeys the principle of reversibility of light. These two laws completely explain the phenomenon of reflection.

• The laws of refraction describe the bending of light when it passes from one transparent medium to another.
• The first law states that the incident ray, refracted ray and the normal at the point of incidence lie in the same plane.
• The second law states that the ratio of sine of angle of incidence to sine of angle of refraction is constant for a given pair of media. This constant is called the refractive index.
• Mathematically, \[\frac{\sin i}{\sin r}=n_{21}\]
• The refractive index depends on the nature of the two media and the wavelength of light. If light travels from rarer to denser medium, it bends towards the normal. These two statements together are known as Snell’s law of refraction.

• Lenses are widely used in daily life, such as in spectacles, peepholes, magnifiers, and telescopes.
• Light passing through a lens undergoes refraction twice: once on entering and once on exiting the lens.
• The shape of a lens affects the direction of light; convex lenses converge light, while concave lenses diverge it.
• Most lenses have surfaces that are parts of spheres, with common types including biconvex, biconcave, plano-convex, and meniscus lenses.

• Magnification is defined as the ratio of the height of the image to the height of the object. It also relates image distance and object distance.
• The magnification produced by a spherical mirror is given by \[m=\frac{h^{\prime}}{h}=-\frac{v}{u}\]
• A negative magnification indicates that the image is real and inverted. A positive magnification indicates that the image is virtual and erect.
• The magnitude of magnification indicates the size of the image relative to the object.
• The formula is valid for both concave and convex mirrors. Proper sign convention must be applied while solving problems.

• When light passes through a curved interface separating two media, refraction occurs at a spherical surface.
• The relation between object distance (u), image distance (v), refractive indices (n₁ and n₂) and radius of curvature (R) is \[\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}\]
• This relation is derived using geometrical approximation for small angles. It is valid for paraxial rays only.
• The Cartesian sign convention must be followed carefully. It applies to any curved refracting surface. This formula forms the basis for deriving the lens maker’s formula.

• Power of a lens is defined as the reciprocal of its focal length in metres.
• It measures the ability of a lens to converge or diverge light rays. Mathematically, \[P=\frac{1}{f}\]
• The SI unit of power is dioptre (D). One dioptre is the power of a lens whose focal length is one metre.
• Convex lenses have positive power. Concave lenses have negative power. Greater the power, smaller is the focal length.

When light passes through a prism, it suffers deviation. The angle of deviation (δ) is given by

δ = i + e − A

At minimum deviation, the refracted ray inside the prism becomes parallel to its base. At this condition,

\[r_1=r_2=\frac{A}{2}\]

The refractive index of the prism is \[n=\frac{\sin\left(\frac{A+D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}\]

This relation is used to determine the refractive index experimentally. The angle of deviation depends on the angle of incidence.

• The magnifying power of a telescope is defined as the ratio of the angle subtended at the eye by the final image to the angle subtended by the object at the unaided eye.
• For an astronomical telescope in normal adjustment, \[m=\frac{f_o}{f_e}\]
• where f_o is focal length of objective and f_e​ is focal length of eyepiece. The objective has a large focal length and large aperture.
• The eyepiece has a small focal length. The final image is formed at infinity. The image formed is inverted. Greater the focal length of objective, greater is the magnifying power.

• The lens maker’s formula gives the focal length of a thin lens in terms of its refractive index and radii of curvature. It is expressed as \[\frac{1}{f}=(n_{21}-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\]
• It is derived by applying refraction at two spherical surfaces of the lens. The formula is valid for thin lenses. R₁ and R₂ are the radii of curvature of the two surfaces.
• The sign convention must be strictly followed. It is useful in designing lenses of required focal length. The formula applies to both convex and concave lenses.

• The mirror formula establishes a mathematical relationship between object distance (u), image distance (v) and focal length (f) of a spherical mirror.
• It is derived using geometrical relations and similar triangles formed by paraxial rays. The formula is expressed as \[\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\]
• It is valid for both concave and convex mirrors. The formula applies to real as well as virtual images. While using this formula, the Cartesian sign convention must be strictly followed.
• It simplifies numerical problems related to image formation by mirrors. This formula is fundamental in ray optics.

• The thin lens formula relates object distance, image distance and focal length of a thin lens. It is given by \[\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\]
• It is valid for both convex and concave lenses. The formula holds for real as well as virtual images.
• It is derived from refraction at spherical surfaces. The Cartesian sign convention must be applied correctly. It is widely used in solving numerical problems related to lenses.