ICSE Class 9 Physics Chapter 07 Reflection of Light

Reflection of Light

Syllabus

(i) Reflection of light; images formed by a pair of parallel and perpendicular plane mirrors. Scope - Laws of reflection; experimental verification; characteristics of images formed in a pair of mirrors (a) parallel and (b) perpendicular to each other; uses of plane mirrors.

(ii) Spherical mirrors; characteristics of image formed by these mirrors (only simple direct ray diagrams are required). Scope - Brief introduction to spherical mirrors-concave and convex mirrors, centre and radius of curvature, pole and principal axis, focus and focal length, location of images from ray diagram for various positions of a small linear object on the principal axis of concave and convex mirrors; characteristics of images, f = R/2 (without proof); sign convention and direct numerical problems using the mirror formulae are included (Derivation of formula not required). Uses of spherical mirrors. Scale drawing or graphical representation of ray diagram not required.

Laws of Reflection and Formation of Image by a Plane Mirror

Reflection of Light

When a beam of light strikes a surface, a part of it returns into the same medium. The part of light which is returned into the medium is called the reflected light. Thus

The return of light into the same medium after striking a surface is called reflection.

The remaining part of light is either absorbed if the surface on which the light strikes is opaque or it is partly transmitted and partly absorbed if the surface is transparent.

It is the reflection of light which enables us to see the different objects around us. An object is seen when light from it enters our eyes. The luminous bodies which emit light by themselves are directly seen, but the non-luminous objects are seen only when they reflect the light incident on them and reflected light reaches our eyes.

Different surfaces reflect light to different extent. A highly polished and silvered surface, such as a plane mirror, reflects almost the entire light falling on it.

A plane mirror is made from a few mm thick glass plate. One surface of glass plate is polished to a high degree of smoothness. This forms the front surface of mirror and the other (or back) surface is silvered (i.e., silver, mercury or some suitable material is deposited over it). The silvered surface is further coated with some opaque material so as to protect the silvering on it. The two surfaces of plane mirror are shown in Fig. 7.1. Light enters from the side of polished surface and is strongly reflected from the silvered surface. The coating serves as an opaque surface and it does not reflect the light.

Kinds of reflection: There are the following two kinds of reflection:

(i) Regular reflection, and
(ii) Irregular reflection.

(i) Regular reflection: Regular reflection occurs when a beam of light falls on a smooth and polished surface, such as a plane mirror. In

Teacher's Note

You see your clear reflection in a mirror because light rays bounce off the smooth surface at the same angles they hit it, which is exactly what we'll learn about in this chapter.

Some Terms Related With Reflection

(i) Incident ray: The light ray striking a reflecting surface is called the incident ray.

(ii) Point of incidence: The point at which the incident ray strikes the reflecting surface, is called the point of incidence.

(iii) Reflected ray: The light ray obtained after reflection from the surface, in the same medium in which the incident ray is travelling, is called the reflected ray.

(iv) Normal: The perpendicular drawn to the surface at the point of incidence, is called the normal.

(v) Angle of incidence: The angle which the incident ray makes with the normal at the point of incidence, is called the angle of incidence. It is denoted by the letter i.

(vi) Angle of reflection: The angle which the reflected ray makes with the normal at the point of incidence, is called the angle of reflection. It is denoted by the letter r.

(vii) Plane of incidence: The plane containing the incident ray and the normal, is called the plane of incidence.

(viii) Plane of reflection: The plane containing the reflected ray and the normal, is called the plane of reflection.

In Fig. 7.3, MM₁ is a plane reflecting surface (say, a plane mirror) kept perpendicular to the plane of paper. A light ray is incident in the direction AO at the point O on mirror. It is reflected along the direction OB. Thus, AO is the incident ray, O is the point of incidence and OB is the reflected ray.

Let ON be the normal (or perpendicular) drawn to the surface MM₁ at the point O. The angle i = ∠AON, which the incident ray makes with the normal, is the angle of incidence and the angle r = ∠BON, which the reflected ray makes with the normal, is the angle of reflection. The plane of paper is the plane of incidence.

Laws of Reflection

A light ray obeys the following two laws for reflection from a surface, which are called the laws of reflection.

(1) The angle of incidence i is equal to the angle of reflection r (i.e., ∠i = ∠r).

In Fig. 7.3, ∠AON = ∠BON ... (7.1)

(2) The incident ray, the reflected ray and the normal at the point of incidence, lie in the same plane.

In Fig. 7.3, AO, ON and OB are in one plane (i.e., the plane of paper).

Reflection of a ray of light normally incident on a plane mirror

For a ray incident normally on a plane mirror, the angle of incidence i = 0°, therefore the angle of reflection r = 0°. Thus, a ray of light AO incident normally on a mirror is reflected along the same path OA i.e., it retraces its path as shown in Fig. 7.4.

Experimental Verification of the Laws of Reflection

Experiment: Fix a sheet of white paper on a drawing board and draw a line MM₁ as shown in Fig. 7.5. On this line, take a point O nearly at the middle of it and draw a line OA such that ∠MOA is less than 90° (say, ∠MOA = 60°). Then draw a normal ON on line MM₁ at the point O, and place a small plane mirror vertical by means of a stand with its silvered surface on the line MM₁.

Now fix two pins P and Q at some distance (= 5 cm) apart vertically on line OA, on the board. Keeping eye on other side of normal (but on the same side of mirror), see clearly the images P' and Q' of the pins P and Q. Now fix a pin R such that it is in line with the images P' and Q' of pins P and Q.

Draw small circles on paper around the position of pins as shown in Fig. 7.5. Remove the pins and draw a line OB joining the point O to the pin points S and R.

Observations

From the above observation table, we find that in each case, angle of incidence is equal to the angle of reflection. This verifies the first law of reflection.

The experiment is being performed on a flat drawing board, with mirror normal to the plane of board on which white sheet of paper is being fixed. Since the lower tips of all the four pins lie on the same plane (i.e., the plane of paper), therefore the incident ray, the reflected ray and the normal at the point of incidence, all lie in one plane. This verifies the second law of reflection.

Formation of Image by Reflection

From each point of an illuminated object, rays of light travel in all directions. To find the position of image of an object formed by a mirror after reflection, we need to consider at least two rays of light incident on mirror from a point of object. Each incident ray gets reflected obeying the laws of reflection. The point where the two reflected rays actually meet or they appear to meet (when produced backwards), gives the position of image of that point of object. Thus we can obtain the positions of image of different points of the object. By joining these points, complete image of the object can be obtained.

Types of image can be of two types: (a) real image, and (b) virtual image.

(a) Real image: The image which can be obtained on a screen, is called a real image. It is formed when light rays after reflection actually intersect. It is inverted. For example, for a distant object, the image formed by a concave mirror is real.

(b) Virtual image: The image which cannot be obtained on a screen, is called a virtual image. It is formed when light rays after reflection do not actually intersect, but they appear to diverge from the image. Geometrically, they intersect when they are produced backwards. It is erect. For example, the image of an object formed by a plane mirror or by a convex mirror is virtual.

Distinction between a real and virtual image

Image of a Point Object Formed by a Plane Mirror

In Fig. 7.6, let MM₁ be a plane mirror in front of which a point object O is placed. From the object O, rays of light travel in all directions. To show the formation of image by the plane mirror, we consider two rays from the object O which fall on the mirror MM₁ in directions AC and BD respectively such that ∠CAN₁ = ∠OAN₁ and ∠DBN₂ = ∠OBN₂. Here AN₁ and BN₂ are the normals at the points A and B.

When seen from a position between C and D, the rays between C and D appear to come from some point I behind the mirror. The point I is the image of the object O. To locate the position of I, reflected rays AC and BD are produced backwards and the point where they meet, gives the position of image I. The image is virtual because the reflected rays AC and BD do not actually meet at I, but to our eye they appear to come from the point I.

Image of an Extended Object Formed by a Plane Mirror

In Fig. 7.7, let MM₁ be a plane mirror in front of which an extended object AB is placed. From all points of the object, light rays travel in all directions. We consider only two rays incident on the plane mirror from the end points A and B of the object. Let AP and AQ be the two rays incident on the mirror from the point A of the object which get reflected from the mirror as PP' and QQ' respectively. These reflected rays when produced backwards, meet at a point A'. Thus A' is the virtual image of point A. Similarly, from the point B of object, BR and BS be the two incident rays on the mirror which are reflected as RR' and SS' respectively. The reflected rays RR' and SS' meet at a point B' when produced backwards. Thus, B' is the virtual image of point B. Similarly, for all other points of the object AB, virtual images are formed between A' and B'. Thus A'B' is the virtual image

of the object AB. It is erect and of size equal to that of the object. The normal distance of each point of image behind the mirror is same as the normal distance of the corresponding object point in front of the mirror (i.e., BN = B'N).

Position of Image

The image I is as far behind the mirror as the object O is in front of it i.e., the perpendicular distance of image from the mirror is equal to the perpendicular distance of object from the mirror.

Proof: Fig. 7.8 shows the formation of image of a point object O by a plane mirror MM₁. A ray OP incident normally on the mirror gets reflected by the mirror along the same path (i.e., along FO), since ∠i = 0°, therefore ∠r = 0°. The other incident ray OA gets reflected along AC, such that ∠OAN = ∠NAC where AN is the normal drawn at the point A on mirror MM₁. The reflected rays FO and AC meet at a point I when they are produced backwards. The point I is the virtual image of the point object O. We are to prove that IF = OF.

For the incident ray OA reflected as AC, ∠OAN = angle of incidence i ∠CAN = angle of reflection r By the law of reflection, angle of incidence = angle of reflection or ∠OAN = ∠CAN ... (7.2)

But ∠OAN = ∠AOF (Alternate angles) and ∠CAN = ∠AIF (Corresponding angles) ∴ ∠AOF = ∠AIF ... (7.3) Now consider the triangles AOF and AIF ∠AOF = ∠AIF ∠AFO = ∠AFI (= 90°) and FA is common side. Therefore, the triangles AOF and AIF are congruent. Hence, OF = IF ... (7.4) Since OF is the normal drawn from the object O on the mirror, so the normal distance of the object from the mirror is equal to the normal distance of image from the mirror. Thus,

The image is situated on the normal drawn from the object on the mirror and it is as far behind the mirror as the object is in front of it.

Lateral Inversion

In our daily experience while looking in a mirror, we notice that a ring on the finger of our left hand appears to be in the finger of the right hand of our image as shown in Fig. 7.9. Similarly, the pocket on the left appears to be on the right in the image. This interchange of the left and right sides is called the lateral inversion. Thus,

The interchange of the left and right sides in the image of an object in a plane mirror is called lateral inversion.

Teacher's Note

When you write and hold your paper up to a mirror, it appears backwards - this is lateral inversion, and it's why ambulance workers write their words backward on vehicles so drivers ahead can read it correctly in their rear-view mirrors.

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