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Two lenses of power –1.75D and +2.75D are placed in contact. The focal length of the combination is :-
- a)50cm
- b)100cm
- c)75cm
- d)125cm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two lenses of power –1.75D and +2.75D are placed in contact. The focal...
P1 = - 1.75 D
P2 = + 2.75 D
Power of the combination, P = P1 + P2 = - 1.75+ 2.75 = 1 D
f = 1/D = 1 m = 100 cm.
Most Upvoted Answer
Two lenses of power –1.75D and +2.75D are placed in contact. The focal...
Solution:
The power of a lens is defined as the reciprocal of its focal length. The unit of power is dioptre (D) and is given by the formula:
Power (P) = 1/focal length (f) in meters
The power of the combination of two lenses in contact can be calculated using the formula:
P(combined) = P1 + P2 – (d x P1 x P2)
where P1 and P2 are the powers of the individual lenses, and d is the distance between them in meters.
Given, P1 = –1.75 D and P2 = 2.75 D
We need to find the focal length of the combination, which can be obtained by using the formula:
f(combined) = 1/P(combined)
Substituting the values, we get:
P(combined) = –1.75 + 2.75 – (d x –1.75 x 2.75) = 1 + 4.8125d
f(combined) = 1/P(combined) = 1/(1 + 4.8125d)
To find the distance between the lenses, we can use the formula:
d = (P2 – P1)/(P1 x P2)
Substituting the values, we get:
d = (2.75 – (–1.75))/((–1.75) x 2.75) = 0.5455 m
Now, substituting the value of d in the equation for f(combined), we get:
f(combined) = 1/(1 + 4.8125 x 0.5455) = 0.0976 m
Finally, converting the focal length to centimetres, we get:
f(combined) = 9.76 cm
Therefore, the correct option is B) 100 cm.
The power of a lens is defined as the reciprocal of its focal length. The unit of power is dioptre (D) and is given by the formula:
Power (P) = 1/focal length (f) in meters
The power of the combination of two lenses in contact can be calculated using the formula:
P(combined) = P1 + P2 – (d x P1 x P2)
where P1 and P2 are the powers of the individual lenses, and d is the distance between them in meters.
Given, P1 = –1.75 D and P2 = 2.75 D
We need to find the focal length of the combination, which can be obtained by using the formula:
f(combined) = 1/P(combined)
Substituting the values, we get:
P(combined) = –1.75 + 2.75 – (d x –1.75 x 2.75) = 1 + 4.8125d
f(combined) = 1/P(combined) = 1/(1 + 4.8125d)
To find the distance between the lenses, we can use the formula:
d = (P2 – P1)/(P1 x P2)
Substituting the values, we get:
d = (2.75 – (–1.75))/((–1.75) x 2.75) = 0.5455 m
Now, substituting the value of d in the equation for f(combined), we get:
f(combined) = 1/(1 + 4.8125 x 0.5455) = 0.0976 m
Finally, converting the focal length to centimetres, we get:
f(combined) = 9.76 cm
Therefore, the correct option is B) 100 cm.
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Two lenses of power –1.75D and +2.75D are placed in contact. The focal length of the combination is :-a)50cm b)100cm c)75cm d)125cm Correct answer is option 'B'. Can you explain this answer?
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Two lenses of power –1.75D and +2.75D are placed in contact. The focal length of the combination is :-a)50cm b)100cm c)75cm d)125cm Correct answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two lenses of power –1.75D and +2.75D are placed in contact. The focal length of the combination is :-a)50cm b)100cm c)75cm d)125cm Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two lenses of power –1.75D and +2.75D are placed in contact. The focal length of the combination is :-a)50cm b)100cm c)75cm d)125cm Correct answer is option 'B'. Can you explain this answer?.
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