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Before we look at Mirror Formula, lets look at the basics
What is Object Distance
Distance of Object from Pole is called Object Distance
It is denoted by u
What is Image Distance
Distance of Image formed from Pole of Mirror is called Image Distance
It is denoted by v
What is Focal length
The Distance between focus and the Pole is Called Focal Length
It is denoted by f
What is Mirror Formula
This formula denotes relationship between
- Object Distance(u)
- Image Distance(v)
- Focal length(f)
Note : - We follow the sign convention for mirrors
In the image, the red text is negative, and blue text is positive
Thus,
- If Virtual image is formed, v is positive
- If Real Image is formed, v is negative
- Object Distance (u) is always negative as it is on left side of Mirror
- Focal Length of Concave Mirror is Negative. It is because Focus is in front of mirror
- Focal Length of Convex Mirror is Positive. It is because Focus is behind mirror
In addition to the mirror formula,
we have the magnification formula
What is the magnification formula?
It is Ratio of Height of Image to the Height of Object
Suppose Height of object is h
Height of Image is h'
Magnification is m
So
Magnification = Height of Image/ Height of Object
m = h'/h
Let's do a few examples
Second Formula for Magnification
There is another formula of magnification
Note : - If magnification (m) is positive , It means image formed is virtual and erect
If magnification (m) is negative, It means image formed is real and inverted
Questions
Example 10.1 - A convex mirror used for rear-view on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from this mirror, find the position, nature and size of the image
Example 10.2 - An object, 4.0 cm in size, is placed at 25.0 cm in front of a concave mirror of focal length 15.0 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Find the nature and the size of the image.
Question 1 Page 171 - Find the focal length of a convex mirror whose radius of curvature is 32 cm
Question 2 Page 171 - A concave mirror produces three times magnified (enlarged) real image an object placed at 10 cm in front of it. Where is the image located?
NCERT Question 7 - We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case.
NCERT Question 12 - An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image
NCERT Question 13 - The magnification produced by a plane mirror is +1. What does this mean?
NCERT Question 14 - An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.
NCERT Question 15 - An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image.
