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Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.
Q. Two point objects A and B are 40 cm apart. A convex lens L of focal length 15 cm should be placed in between them such that the images due to the two point objects coincide. If the least distance between L and A is x, then the value of x – 1 is
Correct answer is '9'. Can you explain this answer?
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Directions: The answer to this question is a single-digit integer, ran...
Let VA be the image distance due to the object A. X is the distance between the object A and the lens.
image due to the second object:
As one of the images should be virtual in order to satisfy the given condition.
the lesser value is 10. Hence, the value of x-1 = 9Most Upvoted Answer
Directions: The answer to this question is a single-digit integer, ran...
Given:
- Distance between point objects A and B = 40 cm
- Focal length of convex lens L = 15 cm
To find:
- The least distance between L and A, denoted as x
- The value of x - 1
Solution:
1. When an object is placed at a distance greater than twice the focal length of a convex lens, a real and inverted image is formed on the other side of the lens.
2. The distance between the object and the lens is called the object distance (denoted as u), and the distance between the image and the lens is called the image distance (denoted as v).
3. According to the lens formula, 1/f = 1/v - 1/u, where f is the focal length of the lens.
4. In this case, we want the images formed by point objects A and B to coincide, which means they should have the same image distance v.
5. Let's consider the distance between lens L and point object A as y. The distance between lens L and point object B would then be (40 - y).
6. Using the lens formula, we can write equations for the two point objects:
- For point object A: 1/15 = 1/v - 1/y
- For point object B: 1/15 = 1/v - 1/(40 - y)
7. Solving these two equations simultaneously will give us the values of v and y.
8. To find the least distance between L and A (x), we need to minimize y.
9. To minimize y, we need to maximize (40 - y) because y and (40 - y) are complementary.
10. The maximum value of (40 - y) occurs when y is minimized, which is when y = 0.
11. Substituting y = 0 in the equation for point object B, we get: 1/15 = 1/v - 1/40
12. Solving this equation will give us the value of v.
13. Once we have the value of v, we can find the least distance between L and A (x) by subtracting it from the focal length of the lens (15 cm).
14. The value of x - 1 can then be calculated by subtracting 1 from x.
Calculations:
- Substituting y = 0 in the equation for point object B: 1/15 = 1/v - 1/40
- Simplifying the equation: 1/v = 1/15 + 1/40 = (40 + 15)/(15 * 40) = 55/600 = 11/120
- Taking the reciprocal of both sides: v = 120/11 cm
- The least distance between L and A (x) = 15 - v = 15 - (120/11) = (165 - 120)/11 = 45/11 cm
- The value of x - 1 = (45/11) - 1 = (45 - 11)/11 = 34/11 = 3 remainder 1
- The answer is the remainder, which is 1.
Answer:
The value of x - 1 is 1.
- Distance between point objects A and B = 40 cm
- Focal length of convex lens L = 15 cm
To find:
- The least distance between L and A, denoted as x
- The value of x - 1
Solution:
1. When an object is placed at a distance greater than twice the focal length of a convex lens, a real and inverted image is formed on the other side of the lens.
2. The distance between the object and the lens is called the object distance (denoted as u), and the distance between the image and the lens is called the image distance (denoted as v).
3. According to the lens formula, 1/f = 1/v - 1/u, where f is the focal length of the lens.
4. In this case, we want the images formed by point objects A and B to coincide, which means they should have the same image distance v.
5. Let's consider the distance between lens L and point object A as y. The distance between lens L and point object B would then be (40 - y).
6. Using the lens formula, we can write equations for the two point objects:
- For point object A: 1/15 = 1/v - 1/y
- For point object B: 1/15 = 1/v - 1/(40 - y)
7. Solving these two equations simultaneously will give us the values of v and y.
8. To find the least distance between L and A (x), we need to minimize y.
9. To minimize y, we need to maximize (40 - y) because y and (40 - y) are complementary.
10. The maximum value of (40 - y) occurs when y is minimized, which is when y = 0.
11. Substituting y = 0 in the equation for point object B, we get: 1/15 = 1/v - 1/40
12. Solving this equation will give us the value of v.
13. Once we have the value of v, we can find the least distance between L and A (x) by subtracting it from the focal length of the lens (15 cm).
14. The value of x - 1 can then be calculated by subtracting 1 from x.
Calculations:
- Substituting y = 0 in the equation for point object B: 1/15 = 1/v - 1/40
- Simplifying the equation: 1/v = 1/15 + 1/40 = (40 + 15)/(15 * 40) = 55/600 = 11/120
- Taking the reciprocal of both sides: v = 120/11 cm
- The least distance between L and A (x) = 15 - v = 15 - (120/11) = (165 - 120)/11 = 45/11 cm
- The value of x - 1 = (45/11) - 1 = (45 - 11)/11 = 34/11 = 3 remainder 1
- The answer is the remainder, which is 1.
Answer:
The value of x - 1 is 1.
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Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. Two point objects A and B are 40 cm apart. A convex lens L of focal length 15 cm should be placed in between them such that the images due to the two point objects coincide. If the least distance between L and A is x, then the value of x – 1 isCorrect answer is '9'. Can you explain this answer?
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Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. Two point objects A and B are 40 cm apart. A convex lens L of focal length 15 cm should be placed in between them such that the images due to the two point objects coincide. If the least distance between L and A is x, then the value of x – 1 isCorrect answer is '9'. 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 Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. Two point objects A and B are 40 cm apart. A convex lens L of focal length 15 cm should be placed in between them such that the images due to the two point objects coincide. If the least distance between L and A is x, then the value of x – 1 isCorrect answer is '9'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. Two point objects A and B are 40 cm apart. A convex lens L of focal length 15 cm should be placed in between them such that the images due to the two point objects coincide. If the least distance between L and A is x, then the value of x – 1 isCorrect answer is '9'. Can you explain this answer?.
Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. Two point objects A and B are 40 cm apart. A convex lens L of focal length 15 cm should be placed in between them such that the images due to the two point objects coincide. If the least distance between L and A is x, then the value of x – 1 isCorrect answer is '9'. 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 Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. Two point objects A and B are 40 cm apart. A convex lens L of focal length 15 cm should be placed in between them such that the images due to the two point objects coincide. If the least distance between L and A is x, then the value of x – 1 isCorrect answer is '9'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. Two point objects A and B are 40 cm apart. A convex lens L of focal length 15 cm should be placed in between them such that the images due to the two point objects coincide. If the least distance between L and A is x, then the value of x – 1 isCorrect answer is '9'. Can you explain this answer?.
Solutions for Directions: The answer to this question is a single-digit integer, ranging from 0 to 9. Enter the correct digit in the box given below.Q. Two point objects A and B are 40 cm apart. A convex lens L of focal length 15 cm should be placed in between them such that the images due to the two point objects coincide. If the least distance between L and A is x, then the value of x – 1 isCorrect answer is '9'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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