Here, the two rays emerging from the object are one parallel to the principal axis and the other passing through the focus of the mirror. These rays, after reflection, form an image at point C. The image formed has the same size as that of the object, and it is real and inverted.

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1. An object is found to be 5 cm in front of a concave mirror with a radius of curvature of 15 cm. Determine the position, nature, and magnification of the image in each case.

The rays considered here are one going parallel to the principal axis and the other passing through the centre of curvature of the mirror. The image formed here is virtual and erect, and it is larger than the object.

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Ray diagrams are necessary for understanding the formation of an image by a concave mirror. For constructing ray diagrams and for a better understanding of image formation, we should consider at least two incident rays coming from the object. The intersection of these two rays after reflection gives the position of the image of the object. For a concave mirror, any of the following four ray diagrams can be used for locating the image formed:

2. An object, 4 cm in size, is placed at 25 cm in front of a concave mirror of focal length 15 cm. At what distance from the mirror should a screen be placed to obtain a sharp image? Determine the nature and the size of the image.

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d) A ray incident obliquely to the principal axis, towards the point P (pole of the mirror), on the concave mirror, is reflected obliquely. The incident and reflected rays follow the laws of reflection at point P, making equal angles with the principal axis.

There is a formation of different images in a concave mirror. It mainly depends on the distance between the object and the mirror. Concave mirrors form both real and virtual images. When the concave mirror is placed very close to the object, a virtual and magnified image is obtained, and if we increase the distance between the object and the mirror, the size of the image reduces and real images are formed. These real images can be projected on a screen. The focal point and the centre of curvature of the concave mirror lie in front of the mirror.

Rays emerging from a point meet at another point after reflection, and this point is called the image of the first point. The image is real if the rays converge to the point, and it is virtual if the rays do not meet it, but appear to diverge from a point when the rays are produced backwards. During image formation, we assume that the rays are paraxial, i.e., they are incident at points close to the pole P of the mirror and make small angles with the principal axis. For a concave mirror, we consider six positions of the object before the mirror.

b) A ray which is passing through the principal focus of a concave mirror, after reflection, will emerge parallel to the principal axis.

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For deriving the relevant formulas for reflection by spherical mirrors, there is a standard sign convention for measuring distances. The normally used convention is the Cartesian sign convention. According to this convention, all the distances are measured from the pole of the mirror, i.e., the pole (P) of the mirror is assumed as the origin. The principal axis of the mirror is taken as the x-axis of the coordinate system. The conventions are as given below:

A negative sign for the value of magnification indicates that the image is real, and a positive sign indicates that the image is virtual.

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In this lesson, we will discuss image formation in concave mirrors. However, before we delve into the topic, let us quickly recall what a concave mirror is and the principles behind its working. A concave mirror is a type of spherical mirror in which the reflecting surface is the inner-curved surface of the sphere, i.e., in this type of mirror, the reflecting surface seems to be away from the incident light source. Because of their shape, the incident light is reflected inwards (converged); thus, they are also called converging mirrors and are used for focusing light.

In a spherical mirror, the distance of the object from its pole is called the object distance (u) and the distance of the image from the pole is called the image distance (v). As mentioned earlier, the distance of the principal focus from the pole is called the focal length (f).

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In this condition, we consider two rays parallel to the principal axis originating from the object. These rays, after reflection, converge and form an image at F, the principal focus of the mirror, in front of the mirror. The image thus formed is highly diminished, point size, real and inverted.

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Both laws of reflection are valid at every point on the curved surface of the mirror. The normal is drawn along the radius, i.e., it is drawn by joining the centre of curvature of the mirror to the point of incidence. The convergence of the rays after reflection is because the normal to the reflecting surface differs at each point on the mirror.

The figure shows two rays emerging from the object. These rays, after reflection, form an image A’B’. From the geometry of ray diagrams, the two right-angled triangles ABF and MPF are similar. This is because, for paraxial rays, the line MP can be considered to be a straight line perpendicular to CP. Therefore,

c) A ray passing through the centre of curvature of a concave mirror, after reflection, is reflected along the same path. The light rays come back along the same path because the incident rays fall on the mirror along the normal to the reflecting surface.

Here, the two rays considered are one parallel to the principal axis and the other passing through the principal focus of the concave mirror. The image is formed beyond C. The image is larger compared to the size of the object, and it is real and inverted.

In this situation, we consider two different rays emerging from the object. One is parallel to the principal axis, and the other is directed towards the centre of curvature of the mirror. These rays, after reflection, form an image between the centre of curvature (C) and the focus (F). The image thus formed is diminished, real and inverted.

Consider a ray parallel to the principal axis striking the concave mirror at a point M on its reflecting surface. Then CM will be perpendicular to the mirror at point M. Let θ be the angle of incidence, and MD be the perpendicular from M to the principal axis.

The rays considered here are one parallel to the principal axis and the other passing through the centre of curvature of the mirror. This results in the formation of a highly enlarged image which is real and inverted at infinity.