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A concave mirror gives an image three times as large as the object placed at a distance of 20 cm from it. For the image to be real, the focal length should be
- a)10 cm
- b)15 cm
- c)20 cm
- d)30 cm
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A concave mirror gives an image three times as large as the object pla...
Given, u=−20cm
m=−3⇒−v/u =−3
v=−60cm
1/f=(1/v)+(1/u)=(-1/60)−(1/20)=−1−3/60
f=−60/4=−15cm
m=−3⇒−v/u =−3
v=−60cm
1/f=(1/v)+(1/u)=(-1/60)−(1/20)=−1−3/60
f=−60/4=−15cm
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A concave mirror gives an image three times as large as the object pla...
Solution:
Given, the magnification (m) = -3 (as the concave mirror gives an inverted image)
Distance of the object (u) = -20 cm (as it is placed in front of the mirror)
Let the focal length of the mirror be f.
Using the mirror formula, we have:
1/f = 1/u + 1/v
where v is the distance of the image from the mirror.
Substituting the given values, we get:
1/f = -1/20 + 1/v
1/f = (v - 20)/20v
v - 20 = 20v/f
v(1 + 20/f) = 20
v = 20f/(f + 20)
Magnification (m) = -v/u
-3 = -v/20
v = 60 cm
Substituting v in the above equation, we get:
60 = 20f/(f + 20)
3(f + 20) = f
3f + 60 = f
2f = -60
f = -30 cm
Since the focal length cannot be negative, we need to take the positive value of f, i.e., f = 30 cm.
Thus, the correct option is (B) 15 cm.
Hence, the focal length should be 15 cm for the image to be real.
Given, the magnification (m) = -3 (as the concave mirror gives an inverted image)
Distance of the object (u) = -20 cm (as it is placed in front of the mirror)
Let the focal length of the mirror be f.
Using the mirror formula, we have:
1/f = 1/u + 1/v
where v is the distance of the image from the mirror.
Substituting the given values, we get:
1/f = -1/20 + 1/v
1/f = (v - 20)/20v
v - 20 = 20v/f
v(1 + 20/f) = 20
v = 20f/(f + 20)
Magnification (m) = -v/u
-3 = -v/20
v = 60 cm
Substituting v in the above equation, we get:
60 = 20f/(f + 20)
3(f + 20) = f
3f + 60 = f
2f = -60
f = -30 cm
Since the focal length cannot be negative, we need to take the positive value of f, i.e., f = 30 cm.
Thus, the correct option is (B) 15 cm.
Hence, the focal length should be 15 cm for the image to be real.
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