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Radius of curvature of concave mirror is 40 cm and the size of real image is twice as that of the object. the object distance is?
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Radius of curvature of concave mirror is 40 cm and the size of real im...
Given:
To find: Object distance
Solution:
The mirror formula is given by:
1/f = 1/v - 1/u
where,
As the given mirror is concave, the focal length is negative. Therefore, f = -40 cm.
Substituting the values in the mirror formula, we get:
1/-40 = 1/v - 1/u
Simplifying the equation, we get:
(v - u)/uv = -1/40
v - u = -uv/40
40v - 40u = -u(v)
40v = u(v-40)
v = 2u
Therefore, the image distance is twice the object distance.
The magnification formula is given by:
m = -v/u
Substituting the value of v, we get:
m = -2
Therefore, the magnification of the mirror is -2, which means the image is inverted and twice the size of the object.
Substituting the value of magnification and image distance in the magnification formula, we get:
m = -v/u
-2 = -2u/u
-2 = -2
Therefore, the object distance is u = 40 cm.
Answer: The object distance is 40 cm.
- Radius of curvature of concave mirror = -40 cm (negative sign indicates concave mirror)
- Size of real image = 2 × size of object
To find: Object distance
Solution:
- Step 1: Use the mirror formula to find the image distance
The mirror formula is given by:
1/f = 1/v - 1/u
where,
- f = focal length of the mirror
- v = image distance
- u = object distance
As the given mirror is concave, the focal length is negative. Therefore, f = -40 cm.
Substituting the values in the mirror formula, we get:
1/-40 = 1/v - 1/u
Simplifying the equation, we get:
(v - u)/uv = -1/40
v - u = -uv/40
40v - 40u = -u(v)
40v = u(v-40)
v = 2u
Therefore, the image distance is twice the object distance.
- Step 2: Use the magnification formula to find the magnification of the mirror
The magnification formula is given by:
m = -v/u
Substituting the value of v, we get:
m = -2
Therefore, the magnification of the mirror is -2, which means the image is inverted and twice the size of the object.
- Step 3: Use the magnification formula again to find the object distance
Substituting the value of magnification and image distance in the magnification formula, we get:
m = -v/u
-2 = -2u/u
-2 = -2
Therefore, the object distance is u = 40 cm.
Answer: The object distance is 40 cm.
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Radius of curvature of concave mirror is 40 cm and the size of real image is twice as that of the object. the object distance is?
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Radius of curvature of concave mirror is 40 cm and the size of real image is twice as that of the object. the object distance is? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Radius of curvature of concave mirror is 40 cm and the size of real image is twice as that of the object. the object distance is? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Radius of curvature of concave mirror is 40 cm and the size of real image is twice as that of the object. the object distance is?.
Radius of curvature of concave mirror is 40 cm and the size of real image is twice as that of the object. the object distance is? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Radius of curvature of concave mirror is 40 cm and the size of real image is twice as that of the object. the object distance is? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Radius of curvature of concave mirror is 40 cm and the size of real image is twice as that of the object. the object distance is?.
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