Reflection | Fun Science https://www.funscience.in Mon, 07 Sep 2020 13:33:19 +0000 en-US hourly 1 https://wordpress.org/?v=6.7.1 Linear Magnification https://www.funscience.in/linear-magnification/ Mon, 24 Aug 2020 08:46:52 +0000 https://www.funscience.in/?p=2268

The linear magnification or magnification of a spherical mirror may be defined as the ratio of the size (height) of the image to the size (height) of the object.

The magnification of a mirror is represented by the letter m.

Thus
m    =    Magnification Of Spherical Mirror Formula

Or
m    =    Magnification Of Spherical Mirror Formula

where,   h2 = size of image
h1 = size of object

As the object is always placed above the principal axis so the magnitude of h1 is always positive. But h2 can be positive or negative depending on whether the image formed is virtual or real. As the virtual image is always erect and above the principal axis therefore h2 will be positive. On the other hand, the real image is always inverted and formed below the principal axis so h2 will be negative. Thus magnification m will be positive when h2 is positive (i.e. image formed is virtual and erect) and m will be negative when h2 is negative (i.e. image formed is real and inverted).

Another point to be noted is that if the value of magnification is equal to 1, then the image formed is of the same size as that of object. If the value of magnification is more than 1, then the image formed is enlarged, and if the value of magnification is less than 1, then the image formed is diminished.

The linear magnification (m) of mirror can also be calculated in terms of image distance (v) and object distance (u), if we do not know the size (height) of object and image.

Thus
m    =    Magnification Of Spherical Mirror Formula

Or
m    =    Magnification Of Spherical Mirror Formula

where,   v = image distance
u = object distance

Unit of Magnification

There is no unit of magnification (m) as it is the ratio of two similar quantities.

Test Your Understanding and Answer These Questions:

  1. What do you meant by linear magnification? What is its S.I. unit.
  2. How is linear magnification applicable in plane mirrors?
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Mirror Formula https://www.funscience.in/mirror-formula/ Mon, 24 Aug 2020 08:40:15 +0000 https://www.funscience.in/?p=2263

A mirror formula may be defined as the formula which gives the relationship between the distance of image v, distance of object u, and the focal length of a mirror. It may be written as,

    where,   v = Distance of image from pole of mirror
u = Distance of object from pole of mirror
and,       f = Focal length of the mirror

The mirror formula is applicable both in spherical mirrors (concave mirrors and convex mirrors) and in plane mirrors.

Test Your Understanding and Answer These Questions:

  1. Define mirror formula.
  2. Derive mirror formula of a concave mirrors.
  3. How is mirror formula applicable in plane mirrors?
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New Cartesian Sign Conventions for spherical mirrors https://www.funscience.in/new-cartesian-sign-conventions-for-spherical-mirrors/ Mon, 24 Aug 2020 08:34:14 +0000 https://www.funscience.in/?p=2258

For measuring the various distances in the ray diagrams of reflection by spherical mirrors, we shall adopt the following system of signs called new cartesian sign conventions.

  1. All the distances in a ray diagram of reflection by spherical mirrors are measured from the pole of the spherical mirror.
  2. The distances measured in the direction of incident light are taken as positive.
  3. The distances measured in the direction opposite to the direction of incident light are taken as negative.
  4. The heights measured upwards and perpendiculars to the principal axis of the mirror are taken as positive.
  5. The heights measured downwards and perpendiculars to the principal axis of the mirror are taken as negative.

Test Your Understanding and Answer These Questions:

  1. Write New Cartesian Sign Conventions for spherical mirrors.
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Method to distinguish between plane mirror, concave mirror and convex mirror, without touching them https://www.funscience.in/method-to-distinguish-between-plane-mirror-concave-mirror-and-convex-mirror-without-touching-them/ Mon, 24 Aug 2020 08:30:24 +0000 https://www.funscience.in/?p=2254

To distinguish between a plane mirror, a concave mirror and a convex mirror without touching it, bring each mirror near to your face one by one and note the change in size of the image formed. There can be following three cases.

Case 1 : In plane mirror, if the object is upright, the image is also upright, of same size and does not change in size by moving the mirror towards or away from the face.

Case 2 : In concave mirror, if the object is upright, the image is also upright but magnified and increases in size by moving the mirror away from the face.

Case 3 : In convex mirror, if the object is upright, the image is also upright but diminished and decreases in size by moving the mirror away from the face.

Test Your Understanding and Answer These Questions:

  1. How can you distinguish between a plane mirror, a concave mirror and a convex mirror without touching them?
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Uses of spherical mirrors https://www.funscience.in/uses-of-spherical-mirrors/ Mon, 24 Aug 2020 08:26:32 +0000 https://www.funscience.in/?p=2250

Following are the important uses of spherical mirrors:

  1. The concave mirrors are commonly used as shaving mirrors because when we see our face in the concave mirror then an enlarged and erect image is formed which helps in smooth shaving.
  2. A concave mirror is used as the reflector in search lights, head lights of motor vehicles, solar cookers, torches and in table lamps.
  3. A concave mirror is also used as head mirror by doctors to examine the retina of the eye, ear and throat.
  4. A convex mirror is used in automobiles such as scooters, trucks and buses as rear view mirror to see the traffic behind the vehicle. The reason for it is that a convex mirror has a much wider field of view and the images formed are smaller and erect.
  5. A convex mirror is also used as a reflector in street lamps.

Test Your Understanding and Answer These Questions:

  1. Give various uses of spherical mirrors in our daily life.
  2. Why is concave mirror used as shaving mirror?
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Formation of images by a convex mirror https://www.funscience.in/formation-of-images-by-a-convex-mirror/ Mon, 24 Aug 2020 08:19:42 +0000 https://www.funscience.in/?p=2245

The image formed in a convex mirror is always virtual and erect, whatever be the position of the object. Now, let’s study the types of images formed by a convex mirror

1. When the object is placed at infinity

When the object is placed at infinity, the two rays AD and BE which run parallel to the principal axis gets diverged in the directions DG and EH respectively after getting reflected from the convex mirror. When the diverged rays DG and EH are extended backwards, they intersect each other at the principal focus F.

Therefore, in convex mirror if the object is present at infinity then the image is formed behind the mirror at the principal focus, which is highly diminished, virtual and erect.

2. When the object is placed anywhere between pole and infinity

If the object is placed anywhere between the pole and infinity, a ray of light AD starting from point A of the object which run parallel to the principal axis gets reflected along DX. On producing back, DX appears to come from F. another ray AE from point A of the object which go towards the centre of curvature is reflected back along EA.

These two reflected rays i.e. DX and EA are diverging rays and appears to intersect each other at point A’ when produced back. So in this case the image is formed behind the mirror, between the pole and the principal focus, which is diminished, virtual and erect.

Table: Summary of images formed by a convex mirror

S No. Position of Object Position of Image Size of Image Nature of Image
1. At infinity At the focus F, behind the mirror Highly diminished Virtual and erect
2. Between infinity and the pole P Between P and F, behind the mirror Diminished Virtual and erect

Test Your Understanding and Answer These Questions:

  1. Explain formation of different types of images by a convex mirror with the help of diagrams.
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Formation of different types of images by concave mirror https://www.funscience.in/formation-of-different-types-of-images-by-concave-mirror/ Sun, 23 Aug 2020 08:35:49 +0000 https://www.funscience.in/?p=2194

Different types of images can be formed by a concave mirror by changing the position of the object from the concave mirror. Therefore different types of images are formed when the object is placed

    1. At the infinity
2. Beyond the centre of curvature
3. At the centre of curvature
4. Between centre of curvature and principal focus
5. At the principal focus
6. Between the principal focus and pole

1. Image formed by a concave mirror when the object is placed at infinity

When the object is placed at infinity, the two rays AB and DE running parallel to the principal axis get reflected at point B and E respectively and intersect each other at the principal focus F on the principal axis. Therefore, in this case the image is formed at the principal focus which is highly diminished, real and inverted.

2. When the object is placed beyond the centre of curvature

When the object AB is placed beyond the centre of curvature then a ray of light AD which is parallel to the principal axis and another ray AE which pass through the centre of curvature intersect each other after reflection at point A’ between the focus and centre of curvature. Thus the image formed is between the principal focus F and centre of curvature C, diminished, real and inverted.

3. When the object is placed at the centre of curvature

When the object AB is placed at the centre of curvature C, then a ray of light AD which is parallel to the principal axis and another ray AE which pass through the principal focus intersect each other after reflection at point A’ just below the position of the object. Thus the image formed in this case is at the centre of curvature, of same size as the object, real and inverted.

4. When the object is placed between the centre of curvature and principal focus

When the object AB is placed between the centre of curvature and principal focus, then the ray AD running parallel to the principal axis and another ray AE passing through the principal focus F intersect each other at point A’ beyond the centre of curvature. Thus the image formed in this case is beyond C, enlarged, real and inverted.

5. When the object is placed at principal focus

When the object AB is placed at the principal focus, then the parallel ray of light AD passes through the principal focus F giving us the reflected ray DX. And the second ray of light AE passing through the centre of curvature C is reflected along the same path forming the reflected ray EY. In this case, both the reflected rays i.e. DX and EY become parallel to each other so these rays cannot intersect each other and the image will be formed at infinity. The image formed in this case will be highly enlarged, real and inverted.

6. When the object is placed between the principal focus and the pole

When the object AB is placed between the principal focus and the pole, then the parallel ray of light AD passes through the focus F giving us the reflected ray DX. And the second ray AE passing through the centre of curvature C is reflected along the same path forming the reflected ray EY.

Now, because the reflected ray DX and EY are diverging away from each other, so these cannot intersect each other in front of the mirror. So, the reflected rays DX and EY are extended backward by dotted lines. On extending backwards, these rays appear to intersect each other at point A’ behind the mirror. Thus the image formed in this case is behind the mirror, highly enlarged, virtual and erect.

Table: Summary of images formed by a concave mirror

S No. Position of Object Position of Image Size of Image Nature of Image
1. At infinity At the focus F Highly diminished Real and inverted
2. Beyond the centre of curvature C Between F and C Diminished Real and inverted
3. At the centre of curvature C At C Same size Real and inverted
4. Between C and F Beyond C Enlarged Real and inverted
5. At focus F At infinity Highly enlarged Real and inverted

Test Your Understanding and Answer These Questions:

  1. Explain formation of different types of images by a concave mirror with the help of diagrams.
  2. Where an object should be placed in front of the concave mirror so as to obtain a real image equal to the size of the object?
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Rules for obtaining images formed by spherical mirrors https://www.funscience.in/rules-for-obtaining-images-formed-by-spherical-mirrors/ Sun, 23 Aug 2020 08:29:00 +0000 https://www.funscience.in/?p=2190

The position of the image formed by spherical mirrors can be found by taking two rays of light coming from a point on the object which intersect each other to form an image. Following are the rules which are used for obtaining images formed by spherical mirrors.

       1. A ray of light which run parallel to the principal axis, after reflection, passes through the principal focus F of a concave mirror, or appears to pass through the principal focus of a convex mirror.

 

       2. A ray of light passing through the centre of curvature in a concave mirror or a ray of light going towards the centre of curvature of a convex mirror is reflected back along the same path.

       3. A ray of light passing through the principal focus of a concave mirror or appearing to pass through the principal focus of a convex mirror becomes parallel to the principal axis after reflection.

Test Your Understanding and Answer These Questions:

  1. What are the rules for obtaining images formed by spherical mirrors?
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Focal length of spherical mirrors https://www.funscience.in/focal-length-of-spherical-mirrors/ Sun, 23 Aug 2020 08:24:37 +0000 https://www.funscience.in/?p=2186

IMPORTANT TERMS RELATED WITH SPHRICAL MIRRORS

Centre of Curvature of Spherical Mirros

The centre of curvature of a spherical mirror is the centre of the hollow glass sphere of which the mirror is a part. It is represented by the letter ‘C’. In fig.(a) and fig.(b) C is the centre of curvature of concave mirror and convex mirror respectively. Here one thing worth to be noted is that the centre of curvature of a concave mirror is always in front of it while the centre of curvature of a convex mirror is always behind it.

Pole of Spherical Mirrors

Pole is the middle point or centre of a spherical mirror. It is represented by letter ‘P’.

Radius of Curvature of Spherical Mirrors

The radius of curvature of a spherical mirror is the radius of the hollow glass sphere of which the mirror is a part. It is represented by letter ‘R’. So PC = R.

Aperture of Mirror

The actual size MM’ of a spherical mirror is called the aperture of the mirror. It may be defined as that portion of a spherical mirror from which the reflection of light is actually taking place.

Principal Axis of Spherical Mirrors

The straight line passing through the pole and centre of curvature of a spherical mirror and extending on both sides is called principal axis of the spherical mirror.

 

Principal Focus and Focal Length of a Spherical Mirror

Principal Focus of Spherical Mirrors

The principal focus of a spherical mirror is a point on the principal axis of the spherical mirror at which, the light rays which are parallel to the principal axis actually converge (meet) or appear to diverge after reflection. The principal focus of a spherical mirror is represented by letter F.

Principal Focus of the Concave Mirror

In the case of concave mirror all the light rays which are parallel to the principal axis meet at point F after reflection. So, the principal focus of a concave mirror is a real focus.

 

Principal Focus of the Convex Mirror

In the case of convex mirror, all the light rays which are parallel to the principal axis appear to diverge after reflection as shown in figure (b1). Thus, we extend all the reflected rays in backward direction by dotted lines, so that they appear to meet at point F. this point is the principal focus of a convex mirror. It is a virtual focus because it is obtained by extending the light rays in backward direction.

Focal Length of Spherical Mirrors

The focal length of a spherical mirror is the distance of principal focus from the pole of the mirror. Thus in figure (a1) and (b1), the distance PF is the focal length of a spherical mirror. The focal length of a spherical mirror is represented by letter ‘f’. So PF = f.

Test Your Understanding and Answer These Questions:

  1. Define center of curvature of a spherical mirror.
  2. Define radius of curvature of a spherical mirror.
  3. Define pole and principal axis of a spherical mirror.
  4. Define principal focus and focal length of a spherical mirror by drawing well labeled diagram.
  5. Give the relationship between focal length and radius of curvature of a spherical mirror.
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Spherical Mirrors https://www.funscience.in/spherical-mirrors/ Sun, 23 Aug 2020 08:17:35 +0000 https://www.funscience.in/?p=2182

Before discussing the reflection of light by spherical mirrors we shall discuss the meaning and types of spherical mirror and some important terms related with spherical mirrors.

Spherical Mirror

A spherical mirror is a part of a hollow sphere of glass whose one side is reflecting while the other side is opaque.

 

     

 

Types of Spherical Mirrors

Spherical mirrors are of two types:

1. Concave mirrors

2. Convex mirrors

Concave Mirrors

A concave mirror is that mirror whose reflecting surface is towards the centre of the glass sphere of which the mirror is a part. In concave mirrors the reflection of light rays takes place from the inner surface while the outer surface is polished and opaque.

 

 

 Convex Mirrors

A convex mirror is that mirror whose reflecting surface is away from the centre of the glass sphere of which the mirror is a part. In convex mirrors the reflection of light rays takes place from the outer surface while the inner surface is opaque.

Test Your Understanding and Answer These Questions:

  1. Define spherical mirror.
  2. Write two types of spherical mirrors.
  3. What is a concave mirror?
  4. What is a convex mirror?
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