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Refraction of light by Spherical Lenses

01-MAR-2016 12:04

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    Refraction is the change in direction of light when it passes from one medium to another. The working of a lens is based on the refraction of light when they pass through it. Lens is a transparent glass which is bounded by two spherical surfaces. The light rays are refracted after passing through the lens. It is of two types, convex lens and concave lens.

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    Convex lens: This lens bulges out at the centre and is thinner at the edges, i.e. the two sides.

    Concave lens: This lens is thinner at the centre and thick at the two sides.

    Optical centre: The centre point of a lens is called optical centre. The ray of light passing through optical centre goes straight and does not deviate.

    Principal axis: A line passing straight through the optical centre in such a way that it is perpendicular to its sides from the centre, it is called principal axis.

    Principal focus of a convex lens: It is a point on the principal axis of the convex lens where all the light rays parallel to the principal axis converge after passing through the lens.

    If the light rays are coming from left hand side they will converge at right hand side of the lens and vice versa. That is why, a lens has two foci. They are at equal distance from the optical centre.

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

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    Focal length of a lens depends on the refractive index of the glass and its curvature. In case of higher refractive index, focal length will be short. Similarly, if the curvature of the lens is more than also the focal length will be short.

    A convex lens is also called converging lens as the parallel beam of light rays passing through it converges at a single point. This can also be shown through an experiment. Place a piece of paper on the ground during sunshine. Now hold a convex lens at some distance above the paper in such a way that a sharp image of sun is formed on the paper. This is the point where all the sunlight is concentrated and the parallel light rays of the sun get converged. In a while you will notice that the heat energy of the focussed sunlight has burned a hole in the paper where the image of sun was formed.

    Principal focus of concave lens:

    All the light rays after passing through the concave lens diverge and when produced backwards appear to meet at a point on the principal axis of the lens. This point is known as principal focus of a concave lens.

    Thus refracted rays appear to diverge from the focus. Concave lens is opposite to convex lens. The parallel beam of light rays is diverged after passing through it. Concave lens also has two foci. If the parallel light rays fall from the left side than they appear to diverge  from a point of the left side only and if the light rays fall from the right hand side that they appear to diverge from a point on right hand side.

    A concave lens is also known as diverging lens. The image formed by this lens is virtual.

    Focal length of concave lens:

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

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    Rules for obtaining images formed by convex lens

    In convex lens, the image is always formed at a point where at least two refracted light rays meet.

    Rule 1: A ray of light which is originally parallel to the principal axis passes through the focus after refraction through the lens.

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    Rule 2: A ray of light passing through the optical centre of the convex lens does not bent after refraction but goes straight. Also, a ray of light going along the path of principal axis of a convex lens also goes straight and does not deviate.

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    Rule 3: When a ray of light passes through the focus of the convex lens then it becomes parallel to the principal axis after refraction through the lens.

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    Types of images formed by a convex lens

    The type of image formed by a convex lens depends on the position of the image.

    Case 1: If the object is placed between optical centre and focus (between C and F’) then the first ray of light starting from the top of the object is parallel to the principal axis. Therefore, as per the rule, it passes through another focus after refraction through the lens. Another ray of light from the object passes through the optical centre of the lens and thus as per the rule goes straight after refraction through the lens. Thus, both the light rays diverge after refraction through the lens and does not meet. Therefore, both the refracted rays are produced backwards so that they meet at a point to form an image.

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    The image formed will be: Behind the object, virtual and erect and larger than the object.

    Case 2: When the object is placed at the focus of the convex lens (at F’) then it means that the object is placed at the distance equal to the focal length of the lens.

    One ray of light becomes parallel to the principal axis of the lens and thus, passes through another focus after refraction through the lens. Another ray of light passes through the optical centre of the lens and goes straight.

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    Therefore, the image formed is: At infinity, Real and inverted, highly enlarged.

    Case 3: When the image is placed between focus and distance less than twice the focal length (F’ and 2F’) then a ray of light parallel to the principal axis of the lens passes through another focus (F) after refraction through the lens. Another ray of light passes through optical centre of the lens and goes straight.

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    Therefore, the image formed is: Real and inverted, Larger than object and beyond 2F.

    Case 4: When the object is paced at the distance equal to twice the focal length ( at 2F’) of the convex lens then one ray of light becomes parallel to the principal axis and passes through another focus of the lens after refraction. Another ray of light passes though optical centre and goes straight after refraction. Both the refracted light rays meet at 2F` on another side.

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    The image formed is: Real and inverted, same size as that of an object.

    Case 5: When the object is placed at the distance greater than twice the focus (beyond 2F’) one ray of light becomes parallel to principal axis and passes through focus after refraction through the lens and another light ray passes through optical centre and goes straight after refraction.

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    The image formed is: Between F and 2F, Real and inverted, Smaller than object.

    Case 6: When the object is placed at infinity, the light rays become parallel after reaching the lens.

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    The image formed is: At the focus on another side, Real and inverted, highly diminished.

    Sign convention for spherical lenses

    According to the New Cartesian Sign Convention:

    i) Distance is measure from the optical centre of the lens.

    ii) The distance measured in the direction same as that of the incident ray are taken as positive.

    iii) The distance measured against the direction of incident ray is taken as negative.

    iv) The distance measured upward and perpendicular to the principal axis is taken as positive.

    v) The distance measured downward and perpendicular to the principal axis is taken as negative.

    vi) The object is always placed on the left hand side of the lens.

    vii) Focal length of convex lens is considered positive.

    viii) Focal length of concave lens is considered negative.

    Lens formula

    1/image distance (v) – 1/object distance (u) = 1/ focal length (f)

    Magnification produced by the lens:

    The size of the image relative to the object is given by the linear magnification. The ratio of the height of the image to the height of the object is called linear magnification.

    Magnification (m) = height of image (h2) /height of object (h1)

    Another formula in terms of distance;

    Magnification = image distance/object distance

    Rules for obtaining images formed by concave lens

    Rule 1: A ray of light parallel to the principal axis of the concave lens appears to be coming from focus after refraction through the lens.

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    Rule 2: A ray of light passing through the optical centre of the concave lens goes straight after refraction through the lens.

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    Rule 3: A ray of light going towards the focus on another side of the concave lens becomes parallel to the principal axis after refraction through the lens.

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    Formation of images by concave lens

    The image formed by concave lens is always: Virtual, Erect and Diminished.

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    Case 1: When an object is placed anywhere between optical centre and infinity, the image formed is between optical centre and focus.

    Case 2: When an object is placed at infinity, the image formed by concave lens will be at focus.

    Power of lens

    A measure of the degree at which a lens can converge or diverge, light rays falling on it is called power of lens.

    Power of lens (P) = 1/ focal length of the lens (f, in meters)

    A lens of short focal length has more power compared to a lens with long focal length. The SI unit of the power of lens is dioptre.

    Power of combination of lenses

    The power of combination of lenses is equal to the algebraic sum of power of individual lenses.

    P = p1 + p2 + p3……..

    The combination of lenses is used in cameras, microscopes, telescopes etc. Combination of lenses increases the sharpness of the image which is free from many defects.

    Image Courtesy: www.ekshiksha.org.in

    Image Courtesy: www.physics.louisville.edu

    Image Courtesy: www.i.kinja-img.com

    DISCLAIMER: JPL and its affiliates shall have no liability for any views, thoughts and comments expressed on this article.

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