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If p , q and r denotes the object distance , image distance and the radius of curvature respectively of a spherical mirror ,then find out the relation between them.?
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Relation between p, q and r for a spherical mirror
When light rays fall on a spherical mirror, they reflect and form an image. The position and size of the image depends on the object distance (p), image distance (q) and the radius of curvature (r) of the mirror. The relationship between these three parameters is given by the mirror formula:
Mirror formula:
1/p + 1/q = 1/r
This formula is applicable for both concave and convex mirrors. Let's see how this formula is derived:
Derivation of the mirror formula:
Consider a spherical mirror of radius of curvature r. Let the object be placed at a distance p from the mirror and the image be formed at a distance q on the other side of the mirror. Let AB be the object and A'B' be the image formed by the mirror.
From the diagram, we can see that:
- OA = r (radius of curvature)
- OB = p (object distance)
- IB' = q (image distance)
- OAB' is a right angled triangle
Using the Pythagorean theorem, we can write:
OA² = OB² + AB²
r² = p² + AB²
AB² = r² - p²
Also, from the geometry of the diagram, we can write:
tan θ = AB/OB
Using the small angle approximation, we can write:
tan θ ≈ θ
Therefore, we can write:
θ = AB/OB
Substituting AB² = r² - p² and θ = AB/OB, we get:
θ = √(r² - p²)/p
Now, using similar triangles OAB' and IAB', we can write:
AB'/IB' = OA/OI
Substituting OA = r and IB' = q, we get:
(r² - p²)/q = r/OI
Solving for OI, we get:
OI = qr/(r - p)
Now, using the definition of magnification, we can write:
m = -IB'/OB
Substituting IB' = q and OB = p, we get:
m = -q/p
Finally, using the definition of magnification and OI, we can write:
m = OI/OB
Substituting OI = qr/(r - p) and OB = p, we get:
m = -qr/(
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If p , q and r denotes the object distance , image distance and the radius of curvature respectively of a spherical mirror ,then find out the relation between them.?
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If p , q and r denotes the object distance , image distance and the radius of curvature respectively of a spherical mirror ,then find out the relation between them.? 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 If p , q and r denotes the object distance , image distance and the radius of curvature respectively of a spherical mirror ,then find out the relation between them.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p , q and r denotes the object distance , image distance and the radius of curvature respectively of a spherical mirror ,then find out the relation between them.?.
If p , q and r denotes the object distance , image distance and the radius of curvature respectively of a spherical mirror ,then find out the relation between them.? 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 If p , q and r denotes the object distance , image distance and the radius of curvature respectively of a spherical mirror ,then find out the relation between them.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p , q and r denotes the object distance , image distance and the radius of curvature respectively of a spherical mirror ,then find out the relation between them.?.
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