ICSE Class 7 Physics Chapter 7 Reflection of Light Spherical Mirrors

7 - Reflection of Light - Spherical Mirrors

Syllabus

1. Spherical mirrors: convex and concave mirrors, centre of curvature, pole, radius of curvature, principal axis, focus of a concave mirror.

2. Image formation by a concave mirror for different positions of the object - drawing ray diagrams for the same.

3. Image formation by a convex mirror - its focus - ray diagrams.

4. Some uses of curved mirrors.

- Formation of an image by a curved mirror - changes observed using objects of different heights, different distances from the mirror; can the image be obtained on a screen? (E).

- Formation of images by a concave mirror (D).

5. Dispersion of light.

Spherical Mirrors

Spherical mirrors: Mirrors that are made by silvering the pieces of glass, which are the part of a hollow sphere, are called spherical mirrors (see Fig. 7.1).

Spherical mirrors may have a concave reflecting surface or a convex reflecting surface. Accordingly, spherical mirrors are of two types.

Concave Mirror

A spherical mirror whose inner hollow concave surface is the reflecting surface (Fig. 7.2 (a)) is called concave mirror.

Convex Mirror

A spherical mirror whose outer surface is the reflecting surface (Fig. 7.2 (b)) is called convex mirror.

Terms Related to Spherical Mirrors

Aperture

The surface of a spherical mirror which is exposed to light for reflection is called its aperture. It is shown by the line MM' (Fig. 7.3).

Pole

The geometric centre of a spherical mirror surface of the mirror is known as the pole of the mirror. It is the mid-point of the aperture of the mirror and is denoted by P (Fig. 7.3).

Centre of Curvature

The geometric centre of the hollow sphere of which the mirror is a part is called the centre of curvature. It is denoted by C.

Radius of Curvature

The radius of the sphere of which the mirror is a part is known as the radius of curvature (PC) of the mirror. It is always denoted by R.

Principal Axis

The straight line passing through the centre of curvature and the pole of a spherical mirror is called the principal axis (PX).

Focus or Focal Point

If a beam of light parallel to the principal axis falls on a concave mirror, all the rays after reflection meet at one point on the principal axis. This point is called the focus of the concave mirror. It is always represented by F (Fig. 7.4).

Similarly, if a beam of light parallel to the principal axis falls on a convex mirror, all the rays after reflection diverge. If the reflected rays are extended backwards, they appear to diverge from a point on the principal axis. This point is called the focus of the convex mirror. It is also represented by F.

Focal Length

The distance between the pole (P) and the focus (F) is called the focal length and is denoted by f.

If f is the focal length and R is the radius of curvature, then, f = R/2 or R = 2f.

This relation is true for both concave and convex mirrors of small aperture and small curvature.

A concave mirror is also called a converging mirror as the parallel rays converge to meet at the focus after reflection.

A convex mirror is called a diverging mirror as the parallel rays appear to diverge from the focus after reflection.

Activity 1

Images Formed by a Spherical Spoon

Take a polished steel spoon. The inside of the spoon is curved inwards and has a concave shape while the outside of the spoon is curved outwards and has a convex shape. Now, hold the spoon in such a way that the inside of the spoon (concave side) is closer to you. See your image (Fig. 7.5(a)). How does your image look like? It is erect and magnified. Keep the spoon at different distances and observe the images.

Now hold the spoon with its outside towards your face, see Fig. 7.5(b). Hold it at different distances and observe the images. You will observe erect and diminished images of yours as you move the spoon away.

Image Formation by Mirrors

A ray diagram gives us an idea about the formation of images by a mirror. Following are some of the important rules for constructing ray diagrams to obtain the images formed by spherical mirrors.

Rules to Draw a Ray Diagram

1. For constructing a ray diagram, we must take at least two rays of convenience whose paths can be traced after reflection.

2. An object is to be kept infront of the reflecting surface and not on the back side.

3. An object is always to be kept on the principal axis such that it is perpendicular to the principal axis and its foot touches the principal axis.

Convenient Rays For The Construction of Image By Ray Diagram

In order to obtain the position and nature of the image formed after reflection from a spherical mirror, we consider at least two rays incident on the mirror from the same point of the object. Although from a point of the object, an infinite number of rays travel in all directions, two rays are chosen according to convenience. Any two of the following rays are taken as the convenient incident rays.

(1) A ray passing through the centre of curvature,

(2) A ray parallel to the principal axis,

(3) A ray passing through the focus,

(4) A ray incident at the pole.

Ray 1: A Ray Passing Through The Centre of Curvature

A ray passing through the centre of curvature after reflection retraces the path i.e. it gets reflected back along the same path (Fig. 7.7).

Ray 2: A Ray Parallel to The Principal Axis

A ray parallel to the principal axis after reflection passes through the principal focus if the mirror is concave (Fig. 7.8a) and appears to diverge from the principal focus if the mirror is convex (Fig. 7.8b).

Ray 3: A Ray Passing Through The Principal Focus

A ray passing through the principal focus in the case of a concave mirror or approaching towards the focus in the case of a convex mirror, is reflected parallel to the principal axis (see Fig. 7.9).

Ray 4: A Ray Incident at The Pole

A ray AP incident at the pole P of the mirror gets reflected along a path PB such that the angle of incidence ∠APC or ∠APC' is equal to the angle of reflection ∠BPC or ∠BPC' (Fig. 7.10). In this case, principal axis itself is normal at pole P.

Images Formed by Concave Mirrors

1. When an Object is at Infinity

When an object is at infinity, the image is formed at focus. It is a real, inverted and highly diminished image (Fig. 7.11).

2. When an Object is Beyond the Centre of Curvature

An object AB is placed beyond the centre of curvature C of the concave mirror (Fig. 7.12). A ray AD is incident on the mirror parallel to the principal axis. This ray after reflection passes through the focus F along DA'. The other ray AE passing through the centre of curvature C gets reflected and retraces its path (i.e., it gets reflected along EA). The two reflected rays DA' and EA intersect at A'. Thus, A' is the real image of the point A. When we take rays incident from other points of the object, we will find that A'B' is the image of AB which is between C and F. The image formed is real, inverted and of smaller size than the object.

3. When an Object is at the Centre of Curvature

An object AB is placed at the centre of curvature C of the concave mirror (Fig. 7.13). A ray AD incident on the mirror parallel to its principal axis gets reflected and passes through the focus F along DA'. The other ray AE incident on the mirror through the focus F gets reflected and becomes parallel to the principal axis along EA'. The two reflected rays DA' and EA' intersect at point A'. Hence, A' is the real image of the point A. In the same way, taking rays incident from other points of the object, A'B' is the image of AB formed at C. The image formed is real, inverted and of the same size as that of the object.

4. When an Object is Between the Centre of Curvature and the Principal Focus

An object AB is placed between focus F and the centre of curvature C of the concave mirror (Fig. 7.14). A ray AD incident on the mirror parallel to the principal axis gets reflected and passes through the point F along DA'. The other ray AE passing through the focus gets reflected and becomes parallel to the principal axis along EA'. The two reflected rays DA' and EA' intersect at A'. Thus, A' is the real image of A. In a similar way, taking rays incident from other points of the object, A'B' is the image of AB formed behind C. The image thus formed is real, inverted and of bigger size than the object.

5. When an Object is Between the Principal Focus and the Pole

An object AB is placed between the pole P and focus F of a concave mirror (Fig. 7.15). A ray AD incident on the mirror parallel to the principal axis after getting reflected, passes through the focus F along DF. The other ray AE passing through the centre of curvature C of the mirror gets reflected and retraces its path (i.e., it gets reflected as EA). The two reflected rays DF and EA do not actually intersect but appear to diverge from A' behind the mirror. These are shown by dotted lines. Thus, A' is the virtual image of A. In a similar way, taking rays incident from other points of the object, A'B' is the image of AB formed behind the mirror. The image formed is virtual, erect and of bigger size than the object.

6. When an Object is at the Principal Focus

When an object is at the principal focus, the image thus formed is at infinity. It is real, inverted and highly magnified (Fig. 7.16).

Table 7.1 Image Formed by a Concave Mirror for Different Positions of the Object

Teacher's Note

When you look at yourself in a concave mirror held close to your face, you see an enlarged, upright image - this is because your face is between the mirror's focus and pole, making it useful for shaving and makeup application.

Images Formed by Convex Mirrors

An object AB is placed in front of a convex mirror. A ray AD incident on the mirror and parallel to the principal axis gets reflected and appears to diverge from focus F along DA1. The other ray AE passing towards the centre of curvature C gets reflected and retraces its path (i.e. it gets reflected back along EA). The two reflected rays DA1 and EA do not actually meet but appear to diverge from at A' behind the mirror as shown by the dotted lines. Thus, A' is the virtual image of the point A. In a similar way, taking rays incident from other points of the object, A'B' is the image of AB.

We must note here that as the object is brought closer to the mirror, the image moves towards the mirror. Its size gets enlarged (but always remains smaller than the size of the object). It is virtual, erect and diminished and is always formed between the pole and focus.

Position, Size and Nature of Image Formed by a Convex Mirror

Teacher's Note

The convex mirror on the back of your car shows you a wide view of traffic behind you while making everything look slightly smaller and farther away - this is why it's labeled "objects in mirror are closer than they appear."

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