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A convex lens forms a real image of an object on a screen; the magnification of the image being 3/2. The object and the screen are kept fixed and the lens is moved through a distance of 16 cm when a sharp image is again formed on the screen; the magnification now being 2/3. What is the focal length of the lens?
  • a)
    19.6 cm
  • b)
    19.2 cm
  • c)
    20 cm
  • d)
    20.4 cm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A convex lens forms a real image of an object on a screen; the magnifi...
3/2=v/u…...1
2/3=(v-16)/(u+16)......2
from these equation
we get v=48, u=32
so now f=(vxu)/(v+u)=96/5=19.2
The correct answer is option B.
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Most Upvoted Answer
A convex lens forms a real image of an object on a screen; the magnifi...
Given:
Magnification of image formed in the first case, m₁ = 3/2
Magnification of image formed in the second case, m₂ = 2/3
Distance through which the lens is moved, u = 16 cm

To find: Focal length of the lens

Using the lens formula, we know that:

1/f = 1/v - 1/u

Where f is the focal length of the lens, v is the distance of the image from the lens and u is the distance of the object from the lens.

Let's assume that the distance of the object from the lens in both cases is u.

Case 1:
Magnification, m₁ = v/u = 3/2
=> v = (3/2)u

Substituting the values of v and u in the lens formula, we get:

1/f = 1/(3/2)u - 1/u
=> 1/f = (1/2u)
=> f = 2u

Case 2:
Magnification, m₂ = v/u = 2/3
=> v = (2/3)u

When the lens is moved through a distance of 16 cm, the new distance of the object from the lens becomes u - 16.

Substituting the values of v, u and u - 16 in the lens formula, we get:

1/f = 1/(2/3)u - 1/(u - 16)
=> 1/f = (3/2u) - (1/(u - 16))

Using the value of f obtained from case 1, we can solve for u:

1/19.2 = (3/2u) - (1/(u - 16))
=> 3(u - 16) - 2u = 19.2u
=> u = 96 cm

Substituting the value of u in the lens formula, we get:

1/f = 1/(2/3)u - 1/(u - 16)
=> 1/f = (3/2u) - (1/(u - 16))
=> 1/f = 0.0156
=> f = 64 cm

Therefore, the focal length of the lens is 19.2 cm (Option B).
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Community Answer
A convex lens forms a real image of an object on a screen; the magnifi...
3/2=v/u
2/3=v-16/u+16
from these eq.we get v=48,u=32
so now f=v*u/v+u=96/5=19.2
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A convex lens forms a real image of an object on a screen; the magnification of the image being 3/2. The object and the screen are kept fixed and the lens is moved through a distance of 16 cm when a sharp image is again formed on the screen; the magnification now being 2/3. What is the focal length of the lens?a)19.6 cmb)19.2 cmc)20 cmd)20.4 cmCorrect answer is option 'B'. Can you explain this answer?
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A convex lens forms a real image of an object on a screen; the magnification of the image being 3/2. The object and the screen are kept fixed and the lens is moved through a distance of 16 cm when a sharp image is again formed on the screen; the magnification now being 2/3. What is the focal length of the lens?a)19.6 cmb)19.2 cmc)20 cmd)20.4 cmCorrect answer is option 'B'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A convex lens forms a real image of an object on a screen; the magnification of the image being 3/2. The object and the screen are kept fixed and the lens is moved through a distance of 16 cm when a sharp image is again formed on the screen; the magnification now being 2/3. What is the focal length of the lens?a)19.6 cmb)19.2 cmc)20 cmd)20.4 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A convex lens forms a real image of an object on a screen; the magnification of the image being 3/2. The object and the screen are kept fixed and the lens is moved through a distance of 16 cm when a sharp image is again formed on the screen; the magnification now being 2/3. What is the focal length of the lens?a)19.6 cmb)19.2 cmc)20 cmd)20.4 cmCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A convex lens forms a real image of an object on a screen; the magnification of the image being 3/2. The object and the screen are kept fixed and the lens is moved through a distance of 16 cm when a sharp image is again formed on the screen; the magnification now being 2/3. What is the focal length of the lens?a)19.6 cmb)19.2 cmc)20 cmd)20.4 cmCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12. Download more important topics, notes, lectures and mock test series for Class 12 Exam by signing up for free.
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