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An observer looks at a tree of height 15 metre with a telescope of magnifying power 10. To him, the tree appears
- a)15 times nearer
- b)10 times nearer
- c)15 times taller
- d)10 times taller
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
An observer looks at a tree of height 15 metre with a telescope of mag...
The angle subtended at the eye becomes 10 times larger.This happens only when the tree appears 10 times nearer.
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An observer looks at a tree of height 15 metre with a telescope of mag...
Explanation:
Magnification power of telescope is given by the formula:
Magnification power = (Angle subtended by the image at the eye) / (Angle subtended by the object at the eye)
In this problem, the magnifying power of the telescope is given as 10. Let us assume that the observer is standing at a distance of x from the tree.
Now, using similar triangles, we can write:
Angle subtended by the image at the eye = Angle subtended by the tree at the eye / 10
Using trigonometry, we can write:
tan(Angle subtended by the tree at the eye) = Height of the tree / Distance of the tree from the observer
tan(Angle subtended by the image at the eye) = Height of the image / Distance of the observer from the image
Substituting the values, we get:
tan(Angle subtended by the image at the eye) = (15/x) / x
tan(Angle subtended by the tree at the eye) = 15/x
Dividing the two equations, we get:
tan(Angle subtended by the image at the eye) / tan(Angle subtended by the tree at the eye) = x/15
tan(Angle subtended by the image at the eye) / tan(Angle subtended by the tree at the eye) = 1/10 (since magnification power = 10)
Therefore, x/15 = 1/10
x = 1.5 metres
Hence, the observer is standing at a distance of 1.5 metres from the tree. Therefore, the tree appears 10 times nearer to the observer. Hence, the correct option is B.
Magnification power of telescope is given by the formula:
Magnification power = (Angle subtended by the image at the eye) / (Angle subtended by the object at the eye)
In this problem, the magnifying power of the telescope is given as 10. Let us assume that the observer is standing at a distance of x from the tree.
Now, using similar triangles, we can write:
Angle subtended by the image at the eye = Angle subtended by the tree at the eye / 10
Using trigonometry, we can write:
tan(Angle subtended by the tree at the eye) = Height of the tree / Distance of the tree from the observer
tan(Angle subtended by the image at the eye) = Height of the image / Distance of the observer from the image
Substituting the values, we get:
tan(Angle subtended by the image at the eye) = (15/x) / x
tan(Angle subtended by the tree at the eye) = 15/x
Dividing the two equations, we get:
tan(Angle subtended by the image at the eye) / tan(Angle subtended by the tree at the eye) = x/15
tan(Angle subtended by the image at the eye) / tan(Angle subtended by the tree at the eye) = 1/10 (since magnification power = 10)
Therefore, x/15 = 1/10
x = 1.5 metres
Hence, the observer is standing at a distance of 1.5 metres from the tree. Therefore, the tree appears 10 times nearer to the observer. Hence, the correct option is B.
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An observer looks at a tree of height 15 metre with a telescope of mag...
The angle subtended at the eye becomes 10 times larger. This happens only when the tree appears 10 times nearer.
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