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An object is placed at a distance of 40 cm in front of a concave mirror of focal length 20 cm. The image produced is
- a)Virtual and inverted
- b)Real and erect
- c)Real, inverted and diminished
- d)Real, inverted and a same size as the object
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
An object is placed at a distance of 40 cm in front of a concave mirro...
Explanation:
When an object is placed at a distance of 40 cm in front of a concave mirror of focal length 20 cm, we need to find the nature and size of the image produced.
Formula:
The formula to find the image produced by a concave mirror is:
1/f = 1/v + 1/u
where,
f = focal length of the mirror
u = distance of object from the mirror
v = distance of image from the mirror
Calculation:
Given, focal length of mirror, f = -20 cm (negative sign represents concave mirror)
Distance of object from mirror, u = -40 cm (negative sign represents object is placed in front of the mirror)
Using the above formula, we can find the distance of the image from the mirror as follows:
1/f = 1/v + 1/u
1/-20 = 1/v + 1/-40
-1/20 = 1/v - 1/40
-1/20 = (40-v)/40v
-v/20 = (40-v)/40v
-v^2 + 40v = -800
v^2 - 40v + 800 = 0
On solving the quadratic equation, we get:
v = 20 cm
So, the image is formed at a distance of 20 cm from the mirror.
To find the nature and size of the image, we can use the mirror formula:
1/f = 1/v + 1/u
1/-20 = 1/20 + 1/u
-1/20 - 1/20 = 1/u
-1/10 = 1/u
u = -10 cm
So, the image is formed at a distance of 10 cm behind the mirror.
Conclusion:
The image is formed at a distance of 10 cm behind the mirror. As the distance of the image is negative, the image is real. The image is formed inverted, as the distance of the object is negative. The size of the image is same as that of the object, as the magnification produced by the mirror is 1. Hence, the correct option is (d) Real, inverted and a same size as the object.
When an object is placed at a distance of 40 cm in front of a concave mirror of focal length 20 cm, we need to find the nature and size of the image produced.
Formula:
The formula to find the image produced by a concave mirror is:
1/f = 1/v + 1/u
where,
f = focal length of the mirror
u = distance of object from the mirror
v = distance of image from the mirror
Calculation:
Given, focal length of mirror, f = -20 cm (negative sign represents concave mirror)
Distance of object from mirror, u = -40 cm (negative sign represents object is placed in front of the mirror)
Using the above formula, we can find the distance of the image from the mirror as follows:
1/f = 1/v + 1/u
1/-20 = 1/v + 1/-40
-1/20 = 1/v - 1/40
-1/20 = (40-v)/40v
-v/20 = (40-v)/40v
-v^2 + 40v = -800
v^2 - 40v + 800 = 0
On solving the quadratic equation, we get:
v = 20 cm
So, the image is formed at a distance of 20 cm from the mirror.
To find the nature and size of the image, we can use the mirror formula:
1/f = 1/v + 1/u
1/-20 = 1/20 + 1/u
-1/20 - 1/20 = 1/u
-1/10 = 1/u
u = -10 cm
So, the image is formed at a distance of 10 cm behind the mirror.
Conclusion:
The image is formed at a distance of 10 cm behind the mirror. As the distance of the image is negative, the image is real. The image is formed inverted, as the distance of the object is negative. The size of the image is same as that of the object, as the magnification produced by the mirror is 1. Hence, the correct option is (d) Real, inverted and a same size as the object.
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An object is placed at a distance of 40 cm in front of a concave mirror of focal length 20 cm. The image produced isa)Virtual and invertedb)Real and erectc)Real, inverted and diminishedd)Real, inverted and a same size as the objectCorrect answer is option 'D'. Can you explain this answer?
Question Description
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An object is placed at a distance of 40 cm in front of a concave mirror of focal length 20 cm. The image produced isa)Virtual and invertedb)Real and erectc)Real, inverted and diminishedd)Real, inverted and a same size as the objectCorrect 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 An object is placed at a distance of 40 cm in front of a concave mirror of focal length 20 cm. The image produced isa)Virtual and invertedb)Real and erectc)Real, inverted and diminishedd)Real, inverted and a same size as the objectCorrect 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 An object is placed at a distance of 40 cm in front of a concave mirror of focal length 20 cm. The image produced isa)Virtual and invertedb)Real and erectc)Real, inverted and diminishedd)Real, inverted and a same size as the objectCorrect answer is option 'D'. Can you explain this answer?.
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