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A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:
- a)0.24 m
- b)0.16 m
- c)1.60 m
- d)0.32 m
Correct answer is option 'D'. Can you explain this answer?
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A concave mirror for face viewing has focal length of 0.4 m. The dista...
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A concave mirror for face viewing has focal length of 0.4 m. The dista...
Given:
Focal length of the concave mirror, f = 0.4 m
Magnification, m = 5
To find:
The distance at which the mirror should be held from the face to see the upright image with a magnification of 5.
Solution:
The magnification of a mirror is given by the formula:
magnification (m) = - (image distance / object distance)
Since we want to see the upright image, the magnification should be positive. Hence, we need to consider the negative sign in the formula.
We know that the focal length of a concave mirror is negative. Therefore, the image distance should be negative.
Let the distance at which the mirror is held from the face be 'd'.
Using the magnification formula, we have:
5 = - (-d / d)
5 = - (-1)
5 = 1
This implies that the object distance (d) is equal to the image distance (-d).
We can now use the mirror formula to find the value of 'd'.
The mirror formula is given by:
1/f = 1/v - 1/u
Where,
f = focal length
v = image distance
u = object distance
Since the image is formed on the same side as the object (virtual image), the image distance (v) is negative.
Substituting the given values in the mirror formula:
1/0.4 = 1/(-d) - 1/d
Simplifying the equation:
2.5 = (-d + d) / (-d * d)
2.5 = 2d / (-d * d)
Cross-multiplying:
-2.5 * d * d = 2d
Simplifying further:
-2.5d^2 = 2d
Dividing both sides by d:
-2.5d = 2
Solving for d:
d = 2 / -2.5
d = -0.8
Since distance cannot be negative, we take the magnitude of d:
d = 0.8 m
Therefore, the distance at which the mirror should be held from the face to see the upright image with a magnification of 5 is 0.8 m.
However, none of the given options match this answer. Therefore, there may be an error in the question or options provided.
Focal length of the concave mirror, f = 0.4 m
Magnification, m = 5
To find:
The distance at which the mirror should be held from the face to see the upright image with a magnification of 5.
Solution:
The magnification of a mirror is given by the formula:
magnification (m) = - (image distance / object distance)
Since we want to see the upright image, the magnification should be positive. Hence, we need to consider the negative sign in the formula.
We know that the focal length of a concave mirror is negative. Therefore, the image distance should be negative.
Let the distance at which the mirror is held from the face be 'd'.
Using the magnification formula, we have:
5 = - (-d / d)
5 = - (-1)
5 = 1
This implies that the object distance (d) is equal to the image distance (-d).
We can now use the mirror formula to find the value of 'd'.
The mirror formula is given by:
1/f = 1/v - 1/u
Where,
f = focal length
v = image distance
u = object distance
Since the image is formed on the same side as the object (virtual image), the image distance (v) is negative.
Substituting the given values in the mirror formula:
1/0.4 = 1/(-d) - 1/d
Simplifying the equation:
2.5 = (-d + d) / (-d * d)
2.5 = 2d / (-d * d)
Cross-multiplying:
-2.5 * d * d = 2d
Simplifying further:
-2.5d^2 = 2d
Dividing both sides by d:
-2.5d = 2
Solving for d:
d = 2 / -2.5
d = -0.8
Since distance cannot be negative, we take the magnitude of d:
d = 0.8 m
Therefore, the distance at which the mirror should be held from the face to see the upright image with a magnification of 5 is 0.8 m.
However, none of the given options match this answer. Therefore, there may be an error in the question or options provided.
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A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:a)0.24 mb)0.16 mc)1.60 md)0.32 mCorrect answer is option 'D'. Can you explain this answer?
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A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:a)0.24 mb)0.16 mc)1.60 md)0.32 mCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:a)0.24 mb)0.16 mc)1.60 md)0.32 mCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:a)0.24 mb)0.16 mc)1.60 md)0.32 mCorrect answer is option 'D'. Can you explain this answer?.
A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:a)0.24 mb)0.16 mc)1.60 md)0.32 mCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:a)0.24 mb)0.16 mc)1.60 md)0.32 mCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:a)0.24 mb)0.16 mc)1.60 md)0.32 mCorrect answer is option 'D'. Can you explain this answer?.
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A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:a)0.24 mb)0.16 mc)1.60 md)0.32 mCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:a)0.24 mb)0.16 mc)1.60 md)0.32 mCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:a)0.24 mb)0.16 mc)1.60 md)0.32 mCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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