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Give the derivation of of spherical mirror formula?
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Give the derivation of of spherical mirror formula?
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Give the derivation of of spherical mirror formula?
Derivation of Spherical Mirror Formula
Introduction
Spherical mirrors are one of the most important optical devices in our daily life. A spherical mirror is a mirror that has a curved surface, and depending on the surface curvature, it can be either a concave or a convex mirror. The formula for spherical mirrors is used to calculate the position, size, and nature of the image formed by a spherical mirror.
Derivation
Let us consider a spherical mirror, such that the radius of curvature of the mirror is R. A point object O is placed at a distance u from the mirror, and its image is formed at a distance v from the mirror, as shown in the figure below:
According to the laws of reflection, the angle of incidence (i) is equal to the angle of reflection (r).
From the diagram above, we have:
i = angle of incidence = angle AOB
r = angle of reflection = angle COB
Also, from the geometry of the figure above, we have:
angle AOB + angle COB = angle AOC = 90 degrees
Therefore, we can write:
i + r = 90 degrees
Using the mirror formula, we can write:
1/v + 1/u = 1/f
where f is the focal length of the mirror.
From the geometry of the figure above, we have:
AB = u
BC = v
OC = R/2
Using the mirror formula, we can write:
1/v + 1/u = 1/f
1/v + 1/u = 1/R - 1/u
1/v = 1/R - 1/u
1/f = 2/R
f = R/2
Conclusion
The formula for spherical mirrors is given by:
1/f = 1/v - 1/u
where f is the focal length of the mirror, v is the distance of the image from the mirror, and u is the distance of the object from the mirror. This formula can be used to calculate the position, size, and nature of the image formed by a spherical mirror.
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Give the derivation of of spherical mirror formula?
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Give the derivation of of spherical mirror formula? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Give the derivation of of spherical mirror formula? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Give the derivation of of spherical mirror formula?.
Give the derivation of of spherical mirror formula? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Give the derivation of of spherical mirror formula? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Give the derivation of of spherical mirror formula?.
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