What are mirrors?
\r\n\n A mirror is a smooth and highly polished surface that reflects light and leads to the formation of an image. When\r\n an object is kept in front of the mirror, it acts as the source of the incident ray, and its image is formed in\r\n the mirror at the point where the reflected rays meet.\n
\r\nSpherical mirrors
\r\n\n Mirrors that have curved reflecting surfaces are called spherical mirrors. A spherical mirror is a part of a\r\n hollow sphere that has been silvered either on the outer or inner surface of the sphere. There are two types of\r\n spherical mirrors depending on whether the inner or outer surface of the sphere is silvered, convex mirrors and\r\n concave mirrors.\n
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Concave Mirror
\r\n A spherical mirror made by silvering its outer surface such that its inner surface acts as the reflecting\r\n surface is known as a concave mirror. A concave mirror is also known as a converging mirror as it\r\n converges\r\n the light rays incident on it after reflection.\r\n \r\n - \n
Convex Mirror
\r\n A spherical mirror made by silvering its inner surface such that its outer surface acts as the\r\n reflecting surface is known as a convex mirror. Its reflecting surface bulges out. A convex mirror is\r\n also known as a diverging mirror as it diverges the light rays incident on it after reflection.\n \r\n
![](\"/assets/mirror_image_1.jpg\")
\r\n Fig: Concave and Convex Mirrors
Features of Spherical Mirrors
\r\n\n Now we will have a look at some important terms related to spherical mirrors that will help us to draw\r\n ray diagrams further in this module.\n
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- \n Centre of curvature (C): It is the centre of the sphere of which the spherical mirror is a part.\r\n \r\n
- Pole (P):The centre of the mirror surface is called the pole. \r\n
- \n Principal Axis:It is an imaginary line perpendicular to the tangent drawn at the pole of\r\n the mirror\r\n and passing through the pole and centre of curvature of the mirror. In the figure shown above line PC represents the principal axis.\r\n \r\n
- \n Aperture (AB):It is the part of the mirror that is exposed to the incident light. It tells us\r\n about the size of the mirror. AB is the aperture of mirror in the figure above.\n \r\n
- Radius of Curvature (R):It is the radius of the sphere the spherical mirror is a part of. \r\n
- \n Focus (F):It is a point on the principal axis from where the incident ray parallel to principal\r\n axis meet or appear to meet after reflection from the mirror. A concave mirror is said to have a\r\n real focus since the light rays incident parallel to principal axis after reflection actually meets\r\n at this point. On the other hand, a convex mirror is said to have a virtual focus since the\r\n light rays after reflection do not actually meet, but they appear to meet at this point.\n \r\n
- \n Focal Length:\r\n It is the distance between the pole and focal point of the mirror. It is equal to half the radius of\r\n curvature of the mirror.\n \r\n
Image Formation in Spherical Mirrors
\r\nREAL AND VIRTUAL IMAGE
\r\n\n When the image of an object is formed by actual intersection of the reflected rays, the image is said to be\r\n real. It is inverted. On the other hand, when the reflected rays do not actually meet, but they appear to meet\r\n when extended, the image formed in this case is called a virtual image. A virtual image is upright.\n
\r\n\r\nCONVENIENT RAYS FOR THE CONSTRUCTION OF AN IMAGE BY A RAY DIAGRAM:
\r\n\n Although there are infinite number of rays coming out from a point of an object but the path of all of these\r\n rays after reflection are not known. Therefore, we look at four convenient rays among them and study about the\r\n path they follow after reflection from the mirror. Any two of the rays listed below can be used to draw the ray\r\n diagrams:\n
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- A ray passing through center of curvature retraces its path after reflection. \r\n
- \n A ray passing through focus or appearing to pass through focus becomes parallel to the principal axis\r\n after reflection from the mirror.\n \r\n
- \n A ray incident parallel to the principal axis after reflection from the mirror passes or appears to\r\n pass through the focus of the mirror.\n \r\n
- \n A ray incident at the pole after reflection makes equal angle with the principal axis as the incident\r\n ray made with the principal axis before reflection.\r\n \r\n
Ray Diagrams for formation of image
\r\n\r\n\n Now we shall study the position and nature of image formed when a small linear object is kept at different\r\n positions in front of the mirror by drawing ray diagrams. Based on the object distance, image formation is\r\n divided into a few cases for convenience. However, you can see the ray diagram and nature of image formed\r\n keeping the object at any distance as you like with the help of magic graph at the end of this module.\n
\r\nImage formation in concave mirror
\r\n\n Below is a table that shows the ray diagram, position, size and nature of the image formed when object is kept\r\n at different positions in front of a concave mirror.\n
\r\n| No. | \r\nPosition of object | \r\nPosition of image | \r\nSize of Image | \r\nNature of Image | \r\nRay Diagram | \r\n
|---|---|---|---|---|---|
| 1. | \r\nAt infinity\t | \r\nAt Focus | \r\nHighly diminished to a point | \r\nReal and inverted | \r\n![](\"/assets/diagram_1.jpg\") | \r\n
| 2. | \r\nBeyond the centre of curvature | \r\nBetween the centre of curvature and focus | \r\nDiminished | \r\nReal and Inverted | \r\n ![](\"/assets/diagram_2.jpg\") | \r\n
| 3. | \r\nAt the centre of curvature | \r\nAt centre of curvature | \r\nSame Size | \r\nReal and inverted | \r\n![](\"/assets/diagram_3.jpg\") | \r\n
| 4. | \r\nBetween the centre of curvature and focus | \r\nBeyond the centre of curvature | \r\nEnlarged | \r\nReal and inverted | \r\n![](\"/assets/diagram_4.jpg\") | \r\n
| 5. | \r\nAt focus | \r\nAt infinity | \r\nHighly enlarged | \r\nReal and inverted | \r\n![](\"/assets/diagram_5.jpg\") | \r\n
| 6. | \r\n\n Between the focus and pole\n | \r\n\n Behind the mirror\n | \r\n\n Enlarged\n | \r\n\n Virtual and upright\n | \r\n![](\"/assets/diagram_6.jpg\") | \r\n
Image formation in convex mirror
\r\nThere are two cases in convex mirror which are listed in the table below.
\r\n| No. | \r\nPosition of object | \r\nPosition of image | \r\nSize of Image | \r\nNature of Image | \r\nRay Diagram | \r\n
|---|---|---|---|---|---|
| 1. | \r\nAt infinity\t | \r\nAt Focus, behind the mirror | \r\nHighly diminished to a point | \r\nVirtual and upright | \r\n![](\"/assets/diagram_8.jpg\") | \r\n
| 2. | \r\n\n At any other position\n | \r\n\n Between pole and focus, behind the mirror\n | \r\n\n Diminished\n | \r\n\n Virtual and upright\n | \r\n![](\"/assets/diagram_7.jpg\") | \r\n
Mirror Formula and Sign convention
\r\n\r\n Now we will study the mirror formula using which we can find the image of an object no matter what is the position\r\n of the object but before we proceed on to study mirror formula let us study about sign conventions using which the\r\n mirror formula is derived and which has to be kept in mind while solving any problem in optics.\r\n
Sign Convention
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- All distances are measured from the pole of the spherical mirror. \r\n
- \n The distances measured in the direction of the incident ray are considered to be positive and the\r\n distances in the direction opposite to incident ray are considered to be negative.\n \r\n
- \tAll measurements of heights above the principal axis are taken to be positive and below are taken to be negative. \r\n
Mirror Formula
\r\n\n The mirror formula is given as:$$\\frac{1}{f}=\\frac{1}{u}+\\frac{1}{v} $$\r\n
Where u is the object distance, v is the image distance and f is the focal length of the mirror.\r\n
It was derived keeping the sign convention in mind,\r\n therefore whenever using this formula the values of u, v and f must be substituted with proper signs according to the sign convention.\n
Magnification
\r\n\n It is the ratio of size of the image to the size of the object. It tells us whether the image formed is enlarged or diminished.\r\n $$m=\\frac{\\text{image height}}{\\text{object height}}=\\frac{h_i}{h_o}=\\frac{-v}{u} \\text{ (on applying sign convention)}$$\r\n where v and u are image and object distance respectively.\r\n Magnification is negative for inverted image and positive for upright image.\n
\r\nPower of a mirror
\r\n\n Power P of a mirror is given as:$$P=\\frac{1}{f}$$\r\n where f is the focal length in meter and is\r\n substituted with proper sign according to the sign convention. Its S.I unit is Dioptre. \n
\n MagicGraph | Image Formation in a Concave Mirror\n
\r\nThis MagicGraph offers a visually interactive assistant that helps student understand the process of image formation in a concave mirror.
\r\nTo Get Started
\r\n\n The MagicGraph shows a concave mirror with an object (candle) placed in front of it. You can change the position of the object\r\n and interactively visualize the position, size and nature of the image formed.\n
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- Move and position the object (AB) in front of the mirror. Note that the position of the object is measured from the pole (P) of the mirror. \r\n
- MagicGraph creates the image of the object (A'B') based on mirror formula. \r\n