Revision: Light >> Refraction Through a Lens Physics (English Medium) ICSE Class 10 CISCE

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.

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'.

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 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.

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.

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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 focus of a lens (often called the principal focus) is a specific point on its principal axis where light rays parallel to the axis either converge or appear to originate from after passing through the lens.

The radius of the sphere, whose part is the lens surface, is called the radius of curvature of that surface of the lens.

It is the line joining the centres of curvature of the two surfaces of the lens.

It is a point on the principal axis of the lens such that a ray of light directed towards this point emerges parallel to its direction of incidence.

For a convex lens, the first focal point is a point F₁ on the principal axis of the lens such that the rays of light coming from it, after refraction through the lens, becomes parallel to the principal axis of the lens.

For a concave lens, the first focal point is a point F₁ on the principal axis of the lens such that the incident rays of light appearing to meet at it, q,fter refraction from the lens become parallel to the principal axis of the lens.

A plane normal to the principal axis, passing through the focus, is called the focal plane.

A plane passing through the first focal point and normal to the principal axis of the lens, is called the first focal plane.

A plane passing through the second focal point and normal to the principal axis of the lens, is called the second focal plane.

The distance of focus (or focal point) from the optical centre of a lens, is called its focal length.

The distance from the optical centre O of the lens to its first focal point F₁ is called the first focal length Ji of the lens.

The distance from the optical centre 0 of the lens to the second focal point F₂ is called the second focal length f₂ of the lens.

For a convex lens, the second focal point is a point F₂ on the principal axis of the lens such that the rays of light incident parallel to the principal axis, after refraction from the lens, pass through it.

For a concave lens, second focal point is a point F₂ on the principal axis of the lens such that the rays of light incident parallel to the principal axis, after refraction from the lens, appear to be diverging from this point.

The centre of the sphere, whose part is the lens surface, is called the centre of curvature of that surface of the lens.

The ratio of the length of image I perpendicular to the principal axis, to the length of object O, is called linear magnification. 

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 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.

The magnification produced by a lens is defined as the ratio of the size of the image to the size of the object, i.e.,
Magnification (m) = `"Size of the image"/"Size of the object"`
It has no unit.

Magnification (m) = \[\frac{\text{Height of the Image}}{\text{Height of the object}}=\frac{h^{\prime}}{h}\]

Magnification in terms of object and image distances:

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

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

\[m=\frac{\mathrm{length~of~image~(I)}}{\mathrm{length~of~object~(O)}}=\frac{\nu}{u}\]

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

• 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.

• A lens can be considered to be made up of a rectangular slab at the centre and a prism on either side.
• A convex lens has prisms with their bases downward in the upper part and upward in the lower part.
• A convex lens has a converging action on incident light rays, bringing them toward a point F.
• A concave lens has a diverging action on the incident light rays, spreading them as if they come from a common point F.

• A ray passing through the optical centre of a lens passes undeviated.
• A ray incident parallel to the principal axis passes through (or appears to come from) the second focus after refraction.
• A real image is formed when refracted rays actually meet and can be obtained on a screen, while a virtual image is formed when rays appear to diverge from a point and cannot be obtained on a screen.

• Pole (mirror) or optical centre (lens) is the origin; principal axis is the X-axis.
• Distances to the right are positive, to the left are negative; heights above the axis are positive, below are negative.
• Concave mirror: $f$ and R are negative; Convex mirror: $f$ and R are positive.
• Real images: image distance and magnification are negative; Virtual images: both are positive.
• Lenses are always negative; they are positive for real images and negative for virtual images; they are positive for convex lenses and negative for concave lenses.

• Convex lenses are used as objective lenses in devices such as telescopes, cameras, and slide projectors to form real, inverted images.
• The eye lens is a convex lens that forms an inverted image on the retina, and the brain interprets it as upright.
• Convex lenses are used in spectacles for hypermetropia, while concave lenses are used for myopia; bifocal lenses have both types for viewing near and far objects.
• A magnifying glass is a convex lens of short focal length, fitted into a frame with a handle, used to view tiny objects.
• To correct chromatic aberration, a combination of concave and convex lenses is used instead of a single convex lens.

• In the distant-object method, a convex lens forms a sharp image of a distant object at its focal plane, yielding an approximate focal length.
• In the auxiliary plane mirror method, the object pin is adjusted to remove parallax with its inverted image; focal length is calculated using:
  f = \[\frac {{x} + {2y}}{2}\]​
• In the optical bench method, the object pin and its inverted image coincide with no parallax when placed at the focal length from the lens.
• In the optical bench method, the focal length is given by:
  f = x₂ − x₁​
  where x₁​ is the pin position, and x₂ is the lens position.
• The image formed in both methods is real, inverted, and the same size as the object when the object is placed at the focus of the lens.