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Reflection of light from Spherical Mirrors

12-FEB-2016 17:36

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    A spherical mirror is that mirror whose reflecting surface is the part of a hollow sphere of glass. Spherical mirrors are of two types: concave mirror and convex mirror. In a concave mirror reflection of light takes place in the bent in surface or concave surface. The inner shiny surface of a spoon is an example of a concave mirror. In a convex mirror the reflection of light takes place at the bulging-out surface or convex surface. The back side of a spoon is an example of convex mirror.

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    Centre of curvature: In a spherical mirror the centre of curvature is the centre point of the hollow sphere of a mirror. In concave mirror, centre of curvature is in front of it but in convex mirror it is behind the mirror.

    Pole: The centre point on the spherical mirror is called pole.

    Radius of curvature: The distance between centre of curvature and pole is called radius of curvature.

    Principal axis: The straight line passing through centre of curvature and pole.

    Aperture of mirror: The portion of mirror from which reflection of light takes place.

    Principal focus of concave mirror: The point on the principal axis to which all the light rays which are parallel to the axis converge after reflection from the concave mirror.

    Focal length of concave mirror: The distance between pole and principal focus.

    Principal focus of a convex mirror: A point on principal axis from which a beam of light rays appear to diverge after being reflected from the convex mirror.

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    Rules for obtaining images formed by concave mirror

    Rule 1: When a ray of light which is parallel to the principal axis gets reflected, it passes through its focus.

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    Rule 2: When a ray of light passes through the centre of curvature, it gets reflected back along the same path.

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    Rule 3: When a ray of light passes through the focus, it becomes parallel to the principal axis after reflection.

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    Rule 4: A ray of light which is incident at the pole is reflected back making the same angle with the principal axis.

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    Formation of image by concave mirror

    Case 1: When an object is placed between the pole and focus (between P & F) of the concave mirror, then the ray of light will pass through focus and centre of curvature. The two reflected rays do not intersect each other on the left side and thus, are produced backwards to form an image. The image formed is:behind the mirror, virtual and errect, larger than the object.

     

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    Case 2: When an object is placed at the focus (at F), the reflected rays of light pass through focus and centre of curvature. The image formed is:at infinity, real and inverted and highly enlarged.

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    Case 3: When an object is placed between focus and centre of curvature (between F & C), the first ray of light passes through focus and second ray of light passes through centre of curvature. When these rays are further extended in the downward direction, the image formed is:real and inverted, larger than the object.

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    Case 4: When an object is placed at the centre of curvature (at C) both the rays pass through focus. The image formed is:at the centre of curvature, real and inverted, same size as that of an object.

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    Case 5: When an object is beyond centre of curvature (beyond C), the image formed is:between F and C, real and inverted, smaller than the object.

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    Case 6: When an object is at infinity (at infinity), the image formed is:at the F, real and inverted, much smaller than the object.

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    Uses of concave mirror

    • As reflectors in torches, vehicle head-lights and search lights to get powerful beams of light.
    • As shaving mirrors.
    • They are used by dentists to see large images of teeth.
    • They are used in the field of solar energy to focus sun’s rays for heating solar furnaces.

    Rules for obtaining images formed by convex mirror

    Rule 1: After reflection, a ray of light parallel to the principal axis appears to be coming from focus.

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    Rule 2: A ray of light going towards centre of curvature is reflected back along the same path.

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    Rule 3: After reflection, a ray of light going towards the focus becomes parallel to the principal axis.

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    Rule 4: Ray of light which is incident at the pole is reflected back making the same angle with the principal axis.

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    Formation of image by convex mirror

    Case 1: When the object is placed anywhere between pole and infinity (between P and infinity), the image formed is:behind the mirror between P and F, virtual and erect, diminished.

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    Case 2: When the object is placed at infinity (at infinity), the image formed is:behind the mirror at F, virtual and erect, highly diminished.

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    Uses of convex mirror

    • Enables driver to view much larger area of the traffic behind him.
    • Big convex mirrors are used as ‘shop security mirrors’.

    Sign convention for Spherical Mirrors

    New Cartesian Sign Convention is used for measuring the various distances in the ray diagrams of spherical mirrors. According to New Cartesian Sign Convention:

    • All the distances are measured from pole of the mirror as origin.
    • Distances are measured in the same direction as that of incident light are taken as positive.
    • Distances measured against the direction of incident light are taken as negative.
    • Distances measured upward and perpendicular to the principal axis are taken as positive.
    • Distances measured downward and perpendicular to the principal axis are taken as negative.

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    The Object is always placed on the left side of the mirror so that the direction of incident light is from left to right. Since the incident light always goes from left to right, all the distances measured from the pole of mirror to the right side will be considered positive. And on the other hand all the distances measured from pole of mirror to the left side will be negative.

    • The image distance (u) is always negative as it is placed to the left side of the mirror.
    • If an image is formed behind a concave mirror (to the right side), the image distance (v) is positive but if the image is formed in front of the mirror (on the left side), then the image distance will be negative.
    • For Convex mirror image distance (v) is always positive as image is always formed on the right hand side.
    • The focal length (f) of a concave mirror is considered negative and for convex mirror it is positive.
    • Height of an object is always considered positive. If an image is formed above the principal axis, its height is taken as positive and if below the principal axis then it is taken as negative.

    Mirror Formula

    A formula which gives the relationship between image distance (v), object distance (u) and focal length (f) of a spherical mirror.

    1/Image distance + 1/ Object distance = 1/ Focal length

    Or 1/v + 1/u = 1/f

    Where v = distance of image from mirror

    u = distance of object from mirror

    f = focal length of the mirror.

    The ratio of the height of image to the height of object is known as linear magnification.

     Magnification = height of image/ height of object

    Or m = h2/h1

    Where m = magnification, h1 = height of image, h1 = height of object

    Height of object (h1) will always be positive. The height (h2) of a virtual image will be positive and that of real image will be negative. In other words, if the magnification has a plus sign, then the image is virtual and erect and if the magnification has a minus sign, then the image is real and inverted.

    Also, the linear magnification produced by a mirror is equal to the ratio of the image distance to the object distance, with a minus sign.

    Magnification =  - Image distance/ Object distance

    Or m = - v/u       

    Where m = magnification, v = image distance, u = object distance

    Therefore, if m = h2/h1 and m = - v/u

    Then, h2/h1 = - v/u

     

    Image Courtesy:www.i.ytimg.com         

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