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Two lenses of power +10D and −5D are placed in contact. Where should an object be held from the lens, so as to obtain a virtual image of magnification 2?
- a)5 cm
- b)-5 cm
- c)10 cm
- d)-10 cm
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two lenses of power +10D and −5D are placed in contact. Where sh...
P1 = +10D, P2 = −5D
P = P1 + P2 = 10−5 = 5D
f = 100/5 = 20cm
Magnification = v/u = 2
v = 2u
P = P1 + P2 = 10−5 = 5D
f = 100/5 = 20cm
Magnification = v/u = 2
v = 2u
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Two lenses of power +10D and −5D are placed in contact. Where sh...
-10D are placed in contact. The combined power of the lenses can be calculated using the lens formula:
1/f = 1/f1 + 1/f2
where f1 and f2 are the focal lengths of the individual lenses.
For a lens with power P (in diopters), the focal length (f) can be calculated as:
f = 1/P
Therefore, for a lens with power 10D, the focal length f1 = 1/10 = 0.1 meters.
Similarly, for a lens with power -10D, the focal length f2 = 1/(-10) = -0.1 meters.
Substituting these values into the lens formula:
1/f = 1/0.1 + 1/(-0.1)
Taking the reciprocal of both sides:
f = 0.1 x (-0.1) / (0.1 - (-0.1))
Simplifying:
f = -0.01 / 0.2
f = -0.05 meters
The combined power of the lenses is given by the reciprocal of the focal length:
P_combined = 1/f = 1/(-0.05) = -20D
Therefore, the combined power of the lenses is -20D.
1/f = 1/f1 + 1/f2
where f1 and f2 are the focal lengths of the individual lenses.
For a lens with power P (in diopters), the focal length (f) can be calculated as:
f = 1/P
Therefore, for a lens with power 10D, the focal length f1 = 1/10 = 0.1 meters.
Similarly, for a lens with power -10D, the focal length f2 = 1/(-10) = -0.1 meters.
Substituting these values into the lens formula:
1/f = 1/0.1 + 1/(-0.1)
Taking the reciprocal of both sides:
f = 0.1 x (-0.1) / (0.1 - (-0.1))
Simplifying:
f = -0.01 / 0.2
f = -0.05 meters
The combined power of the lenses is given by the reciprocal of the focal length:
P_combined = 1/f = 1/(-0.05) = -20D
Therefore, the combined power of the lenses is -20D.
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