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Two thin lenses of power +3.5 D and -2.5 D are placed in contact. Find the focal length of the lens combination.
- a)16.7 m
- b)100 cm
- c)1 cm
- d)-16.7 m
Correct answer is option 'B'. Can you explain this answer?
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Two thin lenses of power +3.5 D and -2.5 D are placed in contact. Find...
Calculation of Focal Length of Lens Combination
Given, power of first lens (P1) = 3.5 D
and power of second lens (P2) = -2.5 D
We know that the formula for calculating the power of a lens is:
P = 1/f
where, P is the power of the lens in diopters and f is the focal length of the lens in meters.
Now, we can calculate the focal length of the two lenses in contact using the formula for the combination of two thin lenses in contact:
1/f = (1/f1) + (1/f2)
where, f1 and f2 are the focal lengths of the individual lenses.
Let's calculate the focal lengths of the two lenses:
Focal length of lens 1 (f1) = 1/P1 = 1/3.5 = 0.2857 m
Focal length of lens 2 (f2) = 1/P2 = 1/-2.5 = -0.4 m (Note: the negative sign indicates that the lens is a diverging lens)
Now, we can substitute the values of f1 and f2 in the formula for the combination of two lenses:
1/f = (1/f1) + (1/f2)
1/f = (1/0.2857) + (1/-0.4)
1/f = 3.5 - 2.5
1/f = 1
Therefore, the focal length of the lens combination is f = 1 m.
Conversion to Centimeters
Since the focal length is in meters, we can convert it to centimeters by multiplying it by 100:
f (in cm) = f (in m) x 100
f (in cm) = 1 x 100
f (in cm) = 100 cm
Hence, the correct answer is option (B) 100 cm.
Given, power of first lens (P1) = 3.5 D
and power of second lens (P2) = -2.5 D
We know that the formula for calculating the power of a lens is:
P = 1/f
where, P is the power of the lens in diopters and f is the focal length of the lens in meters.
Now, we can calculate the focal length of the two lenses in contact using the formula for the combination of two thin lenses in contact:
1/f = (1/f1) + (1/f2)
where, f1 and f2 are the focal lengths of the individual lenses.
Let's calculate the focal lengths of the two lenses:
Focal length of lens 1 (f1) = 1/P1 = 1/3.5 = 0.2857 m
Focal length of lens 2 (f2) = 1/P2 = 1/-2.5 = -0.4 m (Note: the negative sign indicates that the lens is a diverging lens)
Now, we can substitute the values of f1 and f2 in the formula for the combination of two lenses:
1/f = (1/f1) + (1/f2)
1/f = (1/0.2857) + (1/-0.4)
1/f = 3.5 - 2.5
1/f = 1
Therefore, the focal length of the lens combination is f = 1 m.
Conversion to Centimeters
Since the focal length is in meters, we can convert it to centimeters by multiplying it by 100:
f (in cm) = f (in m) x 100
f (in cm) = 1 x 100
f (in cm) = 100 cm
Hence, the correct answer is option (B) 100 cm.
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Two thin lenses of power +3.5 D and -2.5 D are placed in contact. Find the focal length of the lens combination.a)16.7 mb)100 cmc)1 cmd)-16.7 mCorrect answer is option 'B'. Can you explain this answer?
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