Revision: Optics (Ray and Wave Optics) >> Refraction of Light at Spherical Surfaces : Lenses Physics (Theory) ISC (Science) ISC Class 12 CISCE

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.

OR

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.

OR

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

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.

OR

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.

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.

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

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

OR

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

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

OR

A lens is a transparent medium bound by two surfaces.

OR

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

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.

OR

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

OR

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

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 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 plane passing through the focus of a lens and perpendicular to the principal axis is called the 'focal plane'.

The rays travelling parallel to the axis of the lens, after refraction through the lens, either go towards a fixed point on the axis or appear to come from a point. This point is called the 'second focus' or the 'principal focus' of the lens.

The distance of the second focus from the optical centre of the lens is called the 'second focal length' or the 'principal focal length' of the lens.

The rays starting from a fixed point on the principal axis of a lens, or appearing to go towards a fixed point on the axis, after refraction through the lens, become parallel to the principal axis. This point is called the 'first focus' of the lens.

The distance of the first focus from the optical centre of the lens is called the 'first focal-length' of the lens.

The linear magnification produced by a spherical (convex or concave) lens is the ratio of the size of the image formed by the lens to the size of the object, both measured perpendicular to the principal axis.

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

1. Both the Lenses are Convex:
   \[\frac {1}{f}\] = \[\frac {1}{f_1}\] + \[\frac {1}{f_2}\]
2. One Lens is Convex and the Other is Concave:
   \[\frac {1}{f}\] = \[\frac {1}{f_1}\] - \[\frac {1}{f_2}\]
   
3. Combined Power: 
   P = P₁ + P₂

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

\[\frac{n}{v}-\frac{1}{u}=\frac{n-1}{R}\]

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

OR

m = \[\frac {f}{f + u}\]

• 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.

• The optical centre of the lens is taken as the origin; the principal axis is the X-axis and the perpendicular line through the optical centre is the Y-axis.
• Distances to the right of the optical centre are positive and to the left are negative; heights above the principal axis are positive and below are negative.

• Convexo-convex (Bi-convex): Both surfaces are convex; radii of curvature may be equal or different.
• Plano-convex: One surface is plane and the other is convex.
• Concavo-convex (Convex meniscus): One surface is concave and the other convex; thicker at the centre.
• Concavo-concave (Bi-concave): Both surfaces are concave; radii of curvature may be equal or different.
• Plano-concave: One surface is plane, and the other is concave.
• Convexo-concave (Concave meniscus): One surface is convex and the other concave; thinner at the centre.

• The focal length of a lens depends on its refractive index and the radii of curvature of its surfaces (lens maker’s formula).
• Changing the surrounding medium changes a lens's focal length; it increases in a denser medium and may even alter the lens's properties.

• For two coaxial lenses separated by distance d, the equivalent focal length and power depend on f₁, f₂, and d.
• A concave lens always forms a virtual image; therefore, its focal length is determined by combining it with a mirror.
• A convex mirror also always forms a virtual image, so it is combined with a convex lens to find its focal length.
• With a convex lens and a plane mirror, if the object and image coincide without parallax, the object position determines the lens's focal length.
• Focal lengths in lens–mirror combinations are calculated using the lens formula and non-parallax positions.