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A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of combination is
- a)- 1.5 D
- b)- 6.5 D
- c)+ 6.5 D
- d)+ 6.67 D
Correct answer is option 'A'. Can you explain this answer?
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A convex lens of focal length 40 cm is in contact with a concave lens ...
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A convex lens of focal length 40 cm is in contact with a concave lens ...
Given:
- Focal length of convex lens (f1) = 40 cm
- Focal length of concave lens (f2) = -25 cm (negative because it is concave)
To find:
The power of the combination of lenses.
Solution:
The power of a lens is given by the formula: Power (P) = 1/f, where f is the focal length of the lens.
Step 1: Calculate the power of each lens.
- Power of convex lens (P1) = 1/f1 = 1/40 = 0.025 D
- Power of concave lens (P2) = 1/f2 = 1/-25 = -0.04 D
Step 2: Calculate the power of the combination of lenses.
The power of two lenses in contact can be calculated by adding their individual powers.
- Power of combination (P) = P1 + P2 = 0.025 + (-0.04) = -0.015 D
However, the power is usually expressed in positive values, so we convert the negative value to positive.
- Power of combination (P) = |-0.015| = 0.015 D
Step 3: Convert the power to diopters.
Since the power is already in diopters, we don't need to make any further conversions.
Step 4: Compare the calculated power with the given options.
The calculated power of the combination is 0.015 D, which is closest to option 'A' (-1.5 D).
Therefore, the correct answer is option 'A' (-1.5 D).
- Focal length of convex lens (f1) = 40 cm
- Focal length of concave lens (f2) = -25 cm (negative because it is concave)
To find:
The power of the combination of lenses.
Solution:
The power of a lens is given by the formula: Power (P) = 1/f, where f is the focal length of the lens.
Step 1: Calculate the power of each lens.
- Power of convex lens (P1) = 1/f1 = 1/40 = 0.025 D
- Power of concave lens (P2) = 1/f2 = 1/-25 = -0.04 D
Step 2: Calculate the power of the combination of lenses.
The power of two lenses in contact can be calculated by adding their individual powers.
- Power of combination (P) = P1 + P2 = 0.025 + (-0.04) = -0.015 D
However, the power is usually expressed in positive values, so we convert the negative value to positive.
- Power of combination (P) = |-0.015| = 0.015 D
Step 3: Convert the power to diopters.
Since the power is already in diopters, we don't need to make any further conversions.
Step 4: Compare the calculated power with the given options.
The calculated power of the combination is 0.015 D, which is closest to option 'A' (-1.5 D).
Therefore, the correct answer is option 'A' (-1.5 D).
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A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of combination isa)- 1.5 Db)- 6.5 Dc)+ 6.5 Dd)+ 6.67 DCorrect answer is option 'A'. Can you explain this answer?
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