Concept explainers
Part (a) To Determine:
The meaning of the limiting case of spherical mirror is plane mirror.
Answer to Problem 82GP
Solution:
Yes, plane mirror is the limiting case of spherical mirror.
Explanation of Solution
Given Info:
Let height of object be and height of image be
Let Object distance be and Image distance be
Let the focal length of mirror be ‘f’
Formula Used:
Apply focal length formula for spherical mirror
Here, all alphabets are in their usual meanings.
Calculation:
A plane mirror can be considered a limiting case of a spherical mirror.
This will be only applicable when its radius of curvature increases then its surface becomes flatter. When its radius becomes infinity then its focal length will also be infinity and finally it will behave as plane mirror.
Hence, we can say; plane mirror is the limiting case of spherical mirror.
Part (b) To Determine:
The equation related to image and object distances in term of the limit of plane mirror.
Answer to Problem 82GP
Solution:
The equation related to image and object distances in term of the limit of plane mirror is
Explanation of Solution
Given Info:
Let height of object be and height of image be
Let Object distance be and Image distance be
Let the focal length of mirror be ‘f’
Formula Used:
Apply focal length formula for spherical mirror
Here, all alphabets are in their usual meanings.
Calculation:
Apply focal length formula for spherical mirror
This is the required equation.
Part (c) To Determine:
The magnification of plane mirror.
Answer to Problem 82GP
Solution:
The magnification of plane mirror ‘m’ = + 1
Explanation of Solution
Given Info:
Let height of object be and height of image be
Let Object distance be and Image distance be
Let the focal length of mirror be ‘f’
Formula Used:
Magnification of spherical mirror
Here, all alphabets are in their usual meanings.
Calculation:
Apply focal length formula for spherical mirror
Magnification of spherical mirror
In case of plane mirror, we use equation (i)
Magnification of mirror
Part (d) To Determine:
Are the above results consistent.
Answer to Problem 82GP
Solution:
Yes, the result of part (b)and part (c)both are the consistence results in terms of plane mirror which is the limiting case of spherical mirror.
Explanation of Solution
Given Info:
Let height of object be and height of image be
Let Object distance be and Image distance be
Let the focal length of mirror be ‘f’
Formula Used:
Apply focal length formula for spherical mirror
Magnification of spherical mirror
Here, all alphabets are in their usual meanings.
Calculation:
Apply focal length formula for spherical mirror
This is the required equation.
Magnification of spherical mirror
In case of plane mirror, we use equation (i)
Magnification of mirror
From equation (i)and (ii), we conclude that part (b)and part (c)both are the consistent results in terms of plane mirror which is the limiting case of spherical mirror.
Chapter 23 Solutions
Physics: Principles with Applications
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