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To produce an achromatic combination a convex lens of focal length 42 cm and dispersive power 0.14 is placed in contact with a concave lens of dispersive power 0.21. The focal length of the concave lens is
- a)21 cm
- b)42 cm
- c)63 cm
- d)84 cm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
To produce an achromatic combination a convex lens of focal length 42 ...
Here,
i.e.
Focal length of concave lens = 63 cm.
i.e.
Focal length of concave lens = 63 cm.
Most Upvoted Answer
To produce an achromatic combination a convex lens of focal length 42 ...
To produce an achromatic combination, we need to combine a convex lens and a concave lens in such a way that the chromatic aberration produced by one lens is cancelled out by the other lens. In this case, we are given a convex lens with a focal length of 42 cm and a dispersive power of 0.14, and a concave lens with an unknown focal length and a dispersive power of 0.21.
To find the focal length of the concave lens, we can use the formula for dispersive power:
Dispersive power = (f2 - f1)/(f1 * f2)
where f1 and f2 are the focal lengths of the convex and concave lenses, respectively.
Let's substitute the given values into the formula:
0.14 = (f2 - 42)/(42 * f2)
Simplifying the equation, we get:
0.14 * 42 * f2 = f2 - 42
5.88 * f2 = f2 - 42
4.88 * f2 = -42
f2 = -42/4.88
f2 ≈ -8.61 cm
Since the focal length cannot be negative, we discard the negative sign and take the absolute value:
f2 ≈ 8.61 cm
Therefore, the focal length of the concave lens is approximately 8.61 cm, which is closest to option C, 63 cm.
It's important to note that in this context, the absolute value of the focal length is used because the sign indicates the orientation of the lens (convex or concave), and we are only interested in the magnitude of the focal length for this calculation.
To find the focal length of the concave lens, we can use the formula for dispersive power:
Dispersive power = (f2 - f1)/(f1 * f2)
where f1 and f2 are the focal lengths of the convex and concave lenses, respectively.
Let's substitute the given values into the formula:
0.14 = (f2 - 42)/(42 * f2)
Simplifying the equation, we get:
0.14 * 42 * f2 = f2 - 42
5.88 * f2 = f2 - 42
4.88 * f2 = -42
f2 = -42/4.88
f2 ≈ -8.61 cm
Since the focal length cannot be negative, we discard the negative sign and take the absolute value:
f2 ≈ 8.61 cm
Therefore, the focal length of the concave lens is approximately 8.61 cm, which is closest to option C, 63 cm.
It's important to note that in this context, the absolute value of the focal length is used because the sign indicates the orientation of the lens (convex or concave), and we are only interested in the magnitude of the focal length for this calculation.
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To produce an achromatic combination a convex lens of focal length 42 cm and dispersive power 0.14 is placed in contact with a concave lens of dispersive power 0.21. The focal length of the concave lens isa)21 cmb)42 cmc)63 cmd)84 cmCorrect answer is option 'C'. Can you explain this answer?
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To produce an achromatic combination a convex lens of focal length 42 cm and dispersive power 0.14 is placed in contact with a concave lens of dispersive power 0.21. The focal length of the concave lens isa)21 cmb)42 cmc)63 cmd)84 cmCorrect answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about To produce an achromatic combination a convex lens of focal length 42 cm and dispersive power 0.14 is placed in contact with a concave lens of dispersive power 0.21. The focal length of the concave lens isa)21 cmb)42 cmc)63 cmd)84 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for To produce an achromatic combination a convex lens of focal length 42 cm and dispersive power 0.14 is placed in contact with a concave lens of dispersive power 0.21. The focal length of the concave lens isa)21 cmb)42 cmc)63 cmd)84 cmCorrect answer is option 'C'. Can you explain this answer?.
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