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A beam of convergent light coverages to a point 0.5 m in front of the mirror after reflection at a convex mirror, but in the absence of the mirror, the beam converges to a point 0.2m behind the mirror, the radius of curvature of the mirror is?
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A beam of convergent light coverages to a point 0.5 m in front of the ...
u=20
v=20
1/f=1/u+1/v
=1/20+1/20=1/10
f=10 cm
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A beam of convergent light coverages to a point 0.5 m in front of the ...
The given information states that a beam of convergent light converges to a point 0.5 m in front of a convex mirror, but without the mirror, the beam converges to a point 0.2 m behind the mirror. We need to determine the radius of curvature of the mirror.
To solve this problem, we can make use of the mirror formula, which relates the object distance (denoted by 'u'), the image distance (denoted by 'v'), and the focal length (denoted by 'f') of a mirror. The formula is as follows:
1/f = 1/v - 1/u
The focal length of a convex mirror is always negative, so we can rewrite the formula as:
1/f = -1/v + 1/u
Let's assume the radius of curvature of the convex mirror is 'R'. The focal length of the mirror can then be determined using the relation:
f = R/2
The given information states that without the mirror, the beam converges to a point 0.2 m behind the mirror. This implies that the image distance (v) is -0.2 m.
Using the mirror formula, we can substitute the values into the equation:
1/f = -1/v + 1/u
1/(R/2) = -1/(-0.2) + 1/u
Simplifying the equation gives:
2/R = 5 + 1/u
We also know that with the convex mirror in place, the beam converges to a point 0.5 m in front of the mirror. This implies that the object distance (u) is 0.5 m.
Substituting this value into the equation:
2/R = 5 + 1/0.5
Simplifying further gives:
2/R = 5 + 2
2/R = 7
Cross-multiplying the equation gives:
R = 2/7
Therefore, the radius of curvature of the convex mirror is approximately 0.286 m.
In conclusion, the radius of curvature of the convex mirror is 0.286 m.
To solve this problem, we can make use of the mirror formula, which relates the object distance (denoted by 'u'), the image distance (denoted by 'v'), and the focal length (denoted by 'f') of a mirror. The formula is as follows:
1/f = 1/v - 1/u
The focal length of a convex mirror is always negative, so we can rewrite the formula as:
1/f = -1/v + 1/u
Let's assume the radius of curvature of the convex mirror is 'R'. The focal length of the mirror can then be determined using the relation:
f = R/2
The given information states that without the mirror, the beam converges to a point 0.2 m behind the mirror. This implies that the image distance (v) is -0.2 m.
Using the mirror formula, we can substitute the values into the equation:
1/f = -1/v + 1/u
1/(R/2) = -1/(-0.2) + 1/u
Simplifying the equation gives:
2/R = 5 + 1/u
We also know that with the convex mirror in place, the beam converges to a point 0.5 m in front of the mirror. This implies that the object distance (u) is 0.5 m.
Substituting this value into the equation:
2/R = 5 + 1/0.5
Simplifying further gives:
2/R = 5 + 2
2/R = 7
Cross-multiplying the equation gives:
R = 2/7
Therefore, the radius of curvature of the convex mirror is approximately 0.286 m.
In conclusion, the radius of curvature of the convex mirror is 0.286 m.
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A beam of convergent light coverages to a point 0.5 m in front of the mirror after reflection at a convex mirror, but in the absence of the mirror, the beam converges to a point 0.2m behind the mirror, the radius of curvature of the mirror is?
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A beam of convergent light coverages to a point 0.5 m in front of the mirror after reflection at a convex mirror, but in the absence of the mirror, the beam converges to a point 0.2m behind the mirror, the radius of curvature of the mirror is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A beam of convergent light coverages to a point 0.5 m in front of the mirror after reflection at a convex mirror, but in the absence of the mirror, the beam converges to a point 0.2m behind the mirror, the radius of curvature of the mirror is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of convergent light coverages to a point 0.5 m in front of the mirror after reflection at a convex mirror, but in the absence of the mirror, the beam converges to a point 0.2m behind the mirror, the radius of curvature of the mirror is?.
A beam of convergent light coverages to a point 0.5 m in front of the mirror after reflection at a convex mirror, but in the absence of the mirror, the beam converges to a point 0.2m behind the mirror, the radius of curvature of the mirror is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A beam of convergent light coverages to a point 0.5 m in front of the mirror after reflection at a convex mirror, but in the absence of the mirror, the beam converges to a point 0.2m behind the mirror, the radius of curvature of the mirror is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of convergent light coverages to a point 0.5 m in front of the mirror after reflection at a convex mirror, but in the absence of the mirror, the beam converges to a point 0.2m behind the mirror, the radius of curvature of the mirror is?.
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