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A concave mirror gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?
- a)31.2 cm
- b)42 cm
- c)23 cm
- d)-36 cm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A concave mirror gives a real image magnified 6 times when the object ...
As we know that the magnification
And in the second case,
And in the second case,
Most Upvoted Answer
A concave mirror gives a real image magnified 6 times when the object ...
To solve this problem, we can use the mirror formula:
1/f = 1/v - 1/u
where f is the focal length of the mirror, v is the image distance, and u is the object distance.
Let's break down the information given in the problem:
1. A concave mirror gives a real image magnified 6 times:
This tells us that the magnification (M) is 6. The magnification formula is given by:
M = -v/u
Since the image is real, the magnification is positive. Therefore, we have:
6 = -v/u
v = -6u
2. When the object is moved 6 cm, the magnification of the real image is 4 times:
Now, when the object is moved, the new object distance (u') will be u + 6 cm. The new magnification (M') is given as 4. So we have:
4 = -v/u'
v = -4u'
Substituting v = -6u and v = -4u' into the mirror formula, we get:
1/f = 1/(-6u) - 1/u
1/f = -1/u (1/6 - 1)
1/f = -1/u (1 - 1/6)
1/f = -1/u (5/6)
1/f = -5/6u
Similarly,
1/f = 1/(-4u') - 1/u'
1/f = -1/u' (1/4 - 1)
1/f = -1/u' (3/4)
1/f = -3/4u'
Since v = -6u and v = -4u', we can equate them:
-6u = -4u'
6u = 4u'
3u = 2u'
u' = (3/2)u
Substituting u' = (3/2)u into the equation 1/f = -3/4u', we get:
1/f = -3/4u ((2/3)u)
1/f = -1/2u^2
f = -2u^2
Since the focal length cannot be negative, the correct answer is option (D) -36 cm.
1/f = 1/v - 1/u
where f is the focal length of the mirror, v is the image distance, and u is the object distance.
Let's break down the information given in the problem:
1. A concave mirror gives a real image magnified 6 times:
This tells us that the magnification (M) is 6. The magnification formula is given by:
M = -v/u
Since the image is real, the magnification is positive. Therefore, we have:
6 = -v/u
v = -6u
2. When the object is moved 6 cm, the magnification of the real image is 4 times:
Now, when the object is moved, the new object distance (u') will be u + 6 cm. The new magnification (M') is given as 4. So we have:
4 = -v/u'
v = -4u'
Substituting v = -6u and v = -4u' into the mirror formula, we get:
1/f = 1/(-6u) - 1/u
1/f = -1/u (1/6 - 1)
1/f = -1/u (1 - 1/6)
1/f = -1/u (5/6)
1/f = -5/6u
Similarly,
1/f = 1/(-4u') - 1/u'
1/f = -1/u' (1/4 - 1)
1/f = -1/u' (3/4)
1/f = -3/4u'
Since v = -6u and v = -4u', we can equate them:
-6u = -4u'
6u = 4u'
3u = 2u'
u' = (3/2)u
Substituting u' = (3/2)u into the equation 1/f = -3/4u', we get:
1/f = -3/4u ((2/3)u)
1/f = -1/2u^2
f = -2u^2
Since the focal length cannot be negative, the correct answer is option (D) -36 cm.
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A concave mirror gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?a)31.2 cmb)42 cmc)23 cmd)-36 cmCorrect answer is option 'D'. Can you explain this answer?
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A concave mirror gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?a)31.2 cmb)42 cmc)23 cmd)-36 cmCorrect 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 gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?a)31.2 cmb)42 cmc)23 cmd)-36 cmCorrect 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 gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?a)31.2 cmb)42 cmc)23 cmd)-36 cmCorrect answer is option 'D'. Can you explain this answer?.
A concave mirror gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?a)31.2 cmb)42 cmc)23 cmd)-36 cmCorrect 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 gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?a)31.2 cmb)42 cmc)23 cmd)-36 cmCorrect 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 gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?a)31.2 cmb)42 cmc)23 cmd)-36 cmCorrect answer is option 'D'. Can you explain this answer?.
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A concave mirror gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?a)31.2 cmb)42 cmc)23 cmd)-36 cmCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A concave mirror gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?a)31.2 cmb)42 cmc)23 cmd)-36 cmCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A concave mirror gives a real image magnified 6 times when the object is moved 6 cm the magnification of the real image is 4 times. What will be the focal length of the mirror?a)31.2 cmb)42 cmc)23 cmd)-36 cmCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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