Key Terminologies: 1. Pole: The centre of the reflecting surface of a spherical mirror is called the pole. It is represented by 'P'. 2. Centre of Curvature: The centre of the sphere is called the centre of curvature. The spherical mirror is part of a big sphere. The centre of curvature lies outside the mirror. In case of concave mirror it lies in front of the reflective surface. In case of convex mirror it lies behind the reflective surface. 3. Radius of Curvature: The radius of the sphere is called the radius of curvature. It is represented by 'R'. 4. Principal Axis: The line joining the pole and the center of curvature is called the principal axis. 5. Principal Focus: In mirrors with small aperture (diameter) roughly half of the radius of curvature is equal to the focus point. At focus point all the light coming from infinity converge, in case of concave mirrors. The light seem to diverge from f, in case of convex mirrors.

Image Formed by Concave Mirror: (S here stands for distance between object and mirror.):

Image Formed by Concave Mirror: (S here stands for distance between object and mirror.) 1. When S < F, the image is: Virtual, Upright , Magnified (larger) 2. When S = F, the image is formed at infinity. In this case the reflected light rays are parallel and do not meet the others. In this way, no image is formed or more properly the image is formed at infinity. 3. When F < S < 2F, the image is: Real, Inverted (vertically), Magnified (larger) 4. When S = 2F, the image is: Real, Inverted (vertically), Same size 5. When S > 2F, the im5. When S > 2F, the image is: Real, Inverted (vertically), Diminished (smaller) j

USE OF CONCAVE MIRRORS::

USE OF CONCAVE MIRRORS:

IMAGE FORMED BY CONVEX MIRROR::

IMAGE FORMED BY CONVEX MIRROR:

USE OF CONVEX MIRRORS::

USE OF CONVEX MIRRORS:

Sign Convention for Reflection by Spherical Mirrors:

Sign Convention for Reflection by Spherical Mirrors While dealing with the reflection of light by spherical mirrors, we shall follow a set of sign conventions called the New Cartesian Sign Convention. In this convention, the pole (P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis (X’X) of the coordinate system. The conventions are as follows: ( i ) The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side. (ii) All distances parallel to the principal axis are measured from the pole of the mirror. (iii) All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along – x-axis) are taken as negative. (iv) Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive. (v) Distances measured(v) Distances measured perpendicular to and below the principal axis (along –y-axis) are taken as negative.

Mirror Formula and Magnification:

Mirror Formula and Magnification In a spherical mirror, the distance of the object from its pole is called the object distance (u). The distance of the image from the pole of the mirror is called the image distance (v). You already know that the distance of the principal focus from the pole is called the focal length (f). There is a relationship between these three quantities given by the mirror formula which is expressed as 1/v + 1/u = 1/f

MAGNIFICATION::

MAGNIFICATION: Magnification produced by a spherical mirror gives the relative extent to which the image of an object is magnified with respect to the object size. It is expressed as the ratio of the height of the image to the height of the object. It is usually represented by the letter m. If h is the height of the object and h ′ is the height of the image, then the magnification m produced by a spherical mirror is given by m = Height of Image (h') / Height of Object (h) = h' / h The magnification m is also related to the object distance (u) and image distance (v). It can be expressed as: Magnification (m) = h'/h = -v/u

REFRACTION OF LIGHT::

REFRACTION OF LIGHT:

LAWS OF REFRACTION OF LIGHT::

LAWS OF REFRACTION OF LIGHT: ( i ) The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane. (ii) The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of media. This law is also known as Snell’s law of refraction. If i is the angle of incidence and r is the angle of refraction, then, sin i / sin r = constant This constant value is called the refractive index of the second medium with respect to the first.

Refractive Index of Some Media:

Refractive Index of Some Media

REFRACTION BY SPERICAL LENSES::

REFRACTION BY SPERICAL LENSES: A transparent material bound by two surfaces, of which one or both surfaces are spherical, forms a lens. This means that a lens is bound by at least one spherical surface. In such lenses, the other surface would be plane. A lens may have two spherical surfaces, bulging outwards. Such a lens is called a double convex lens. It is simply called a convex lens. It is thicker at the middle as compared to the edges. Convex lens converges light rays, hence convex lenses are called converging lenses. Similarly, a double concave lens is bounded by two spherical surfaces, curved inwards. It is thicker at the edges than at the middle. Such lenses diverge light rays as shown and are called diverging lenses. A double concave lens is simply called a concave lens. A lens, either a convex lens or a concave lens, has two spherical surfaces. Each of these surfaces forms a part of a sphere. The centres of these spheres are called centres of curvature of the lens.

IMAGE FORMED BY CONCAVE ::

IMAGE FORMED BY CONCAVE :

IMAGE FORMED BY CONVEX::

IMAGE FORMED BY CONVEX:

SIGN CONVENTION FOR SPHERICAL LENSES::

SIGN CONVENTION FOR SPHERICAL LENSES:

Lens Formula and Magnification:

Lens Formula and Magnification

MAGNIFICATION::

MAGNIFICATION:

POWER OF LENS::

POWER OF LENS: The degree of convergence or divergence of light rays achieved by a lens is expressed in terms of its power. The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P. The power P of a lens of focal length f is given by: P =1/f

POWER OF LENS::

POWER OF LENS: The SI unit of power of a lens is ‘dioptre’. It is denoted by the letter D. If f is expressed in metres, then, power is expressed in dioptres. Thus, 1 dioptre is the power of a lens whose focal length is 1 metre. 1D = 1m–1. Power of a convex lens is positive and that of a concave lens is negative. Opticians prescribe corrective lenses indicating their powers. Let us say the lens prescribed has power equal to + 2.0 D. This means the lens prescribed is convex. The focal length of the lens is + 0.50 m. Similarly, a lens of power – 2.5 D has a focal length of – 0.40 m. The lens is concave. Many optical instruments consist of a number of lenses. They are combined to increase the magnification and sharpness of the image. The net power (P) of the lenses placed in contact is given by the algebraic sum of the individual powers P1, P2, P3, … as P = P1 + P2 + P3 +…

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