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A combination of two thin convex lens of equal focal length is kept separated along the optic axes by a distance of 20 cm between them. The combination behaves as a lens system of infinite focal length. If an object is kept at 10 cm from the first lens, its image will be formed on the other side at a distance x from the second lens. The value of x is:-
- a)10 cm
- b)20 cm
- c)6.67 cm
- d)infinite
Correct answer is option 'A'. Can you explain this answer?
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A combination of two thin convex lens of equal focal length is kept se...
Given:
- Two thin convex lenses of equal focal length
- Separation between the lenses = 20 cm
- Combination behaves as a lens system of infinite focal length
To Find:
The distance x at which the image is formed from the second lens when the object is kept at 10 cm from the first lens.
Solution:
Step 1: Understanding the Lens System
When two lenses are placed in contact, their combined focal length is given by the formula:
1/f = 1/f1 + 1/f2
In this case, the combination behaves as a lens system of infinite focal length, which means the combined focal length is infinite. Therefore, the individual focal lengths of the lenses cancel each other out.
1/f = 1/f1 + 1/f2 = 0
This implies that f1 = -f2
Step 2: Applying the Lens Formula
The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens.
1/v - 1/u = 1/f
For the first lens:
u1 = -10 cm (negative sign indicates object is on the same side as the incident light)
f1 = -f2 (from Step 1)
1/v1 - 1/u1 = 1/f1
1/v1 + 1/10 = 1/f1
Step 3: Finding the Image Distance
Since the combination behaves as a lens system of infinite focal length, the image formed by the first lens will act as the object for the second lens.
Therefore, the object distance for the second lens is the image distance (v1) obtained from the first lens.
For the second lens:
u2 = v1
f2 = -f1 (from Step 1)
1/v2 - 1/u2 = 1/f2
1/v2 - 1/v1 = 1/f2
Substituting the value of f2 from Step 1:
1/v2 - 1/v1 = 1/-f1
1/v2 - 1/v1 = -1/f1
Step 4: Simplifying the Equation
Substituting the values of f1 and v1 obtained from Step 2:
1/v2 - 1/10 = -1/f1
1/v2 - 1/10 = 1/(-f1)
1/v2 - 1/10 = 1/(-(-f2)) [Since f1 = -f2]
1/v2 - 1/10 = 1/f2
Therefore, the equation becomes:
1/v2 - 1/10 = 1/f2
Step 5: Determining the Value of x
Since the combination behaves as a lens system of infinite focal length, the image formed by the second lens will be at infinity.
Therefore, 1/v2 = 0
Substituting this value in the equation from Step 4:
1/0 - 1/10 = 1/f2
-1/10 = 1/f2
Simplifying the equation:
f2 = -10 cm
Since the image is formed on the other side of the second lens, the distance x is equal
- Two thin convex lenses of equal focal length
- Separation between the lenses = 20 cm
- Combination behaves as a lens system of infinite focal length
To Find:
The distance x at which the image is formed from the second lens when the object is kept at 10 cm from the first lens.
Solution:
Step 1: Understanding the Lens System
When two lenses are placed in contact, their combined focal length is given by the formula:
1/f = 1/f1 + 1/f2
In this case, the combination behaves as a lens system of infinite focal length, which means the combined focal length is infinite. Therefore, the individual focal lengths of the lenses cancel each other out.
1/f = 1/f1 + 1/f2 = 0
This implies that f1 = -f2
Step 2: Applying the Lens Formula
The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens.
1/v - 1/u = 1/f
For the first lens:
u1 = -10 cm (negative sign indicates object is on the same side as the incident light)
f1 = -f2 (from Step 1)
1/v1 - 1/u1 = 1/f1
1/v1 + 1/10 = 1/f1
Step 3: Finding the Image Distance
Since the combination behaves as a lens system of infinite focal length, the image formed by the first lens will act as the object for the second lens.
Therefore, the object distance for the second lens is the image distance (v1) obtained from the first lens.
For the second lens:
u2 = v1
f2 = -f1 (from Step 1)
1/v2 - 1/u2 = 1/f2
1/v2 - 1/v1 = 1/f2
Substituting the value of f2 from Step 1:
1/v2 - 1/v1 = 1/-f1
1/v2 - 1/v1 = -1/f1
Step 4: Simplifying the Equation
Substituting the values of f1 and v1 obtained from Step 2:
1/v2 - 1/10 = -1/f1
1/v2 - 1/10 = 1/(-f1)
1/v2 - 1/10 = 1/(-(-f2)) [Since f1 = -f2]
1/v2 - 1/10 = 1/f2
Therefore, the equation becomes:
1/v2 - 1/10 = 1/f2
Step 5: Determining the Value of x
Since the combination behaves as a lens system of infinite focal length, the image formed by the second lens will be at infinity.
Therefore, 1/v2 = 0
Substituting this value in the equation from Step 4:
1/0 - 1/10 = 1/f2
-1/10 = 1/f2
Simplifying the equation:
f2 = -10 cm
Since the image is formed on the other side of the second lens, the distance x is equal
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A combination of two thin convex lens of equal focal length is kept separated along the optic axes by a distance of 20 cm between them. The combination behaves as a lens system of infinite focal length. If an object is kept at 10 cm from the first lens, its image will be formed on the other side at a distance x from the second lens. The value of x is:-a)10 cmb)20 cmc)6.67 cmd)infiniteCorrect answer is option 'A'. Can you explain this answer?
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A combination of two thin convex lens of equal focal length is kept separated along the optic axes by a distance of 20 cm between them. The combination behaves as a lens system of infinite focal length. If an object is kept at 10 cm from the first lens, its image will be formed on the other side at a distance x from the second lens. The value of x is:-a)10 cmb)20 cmc)6.67 cmd)infiniteCorrect answer is option 'A'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A combination of two thin convex lens of equal focal length is kept separated along the optic axes by a distance of 20 cm between them. The combination behaves as a lens system of infinite focal length. If an object is kept at 10 cm from the first lens, its image will be formed on the other side at a distance x from the second lens. The value of x is:-a)10 cmb)20 cmc)6.67 cmd)infiniteCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A combination of two thin convex lens of equal focal length is kept separated along the optic axes by a distance of 20 cm between them. The combination behaves as a lens system of infinite focal length. If an object is kept at 10 cm from the first lens, its image will be formed on the other side at a distance x from the second lens. The value of x is:-a)10 cmb)20 cmc)6.67 cmd)infiniteCorrect answer is option 'A'. Can you explain this answer?.
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