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According to the sign convention, the focal length of a convex lens is ________ and that of a concave lens is ________.
negative; negative
positive; positive
positive; negative
negative; positive
positive; negative
According to the Cartesian sign convention, the focal length (f) of a convex lens is taken as positive because its principal focus lies on the side of the outgoing light rays. Conversely, the focal length of a concave lens is taken as negative because its principal focus lies on the side of the incoming light rays (in front of the lens).
According to the Cartesian sign convention, the focal length (f) of a convex lens is taken as positive because its principal focus lies on the side of the outgoing light rays. Conversely, the focal length of a concave lens is taken as negative because its principal focus lies on the side of the incoming light rays (in front of the lens).
Think of a convex lens as a 'positive' collector that gathers light rays together to a single point, while a concave lens is a 'negative' spreader that pushes light away from a virtual point.
Convex = Positive (+) because it gathers; Concave = Negative (-) because it scatters.
f1тАЛ=v1тАЛтИТu1тАЛ тАФ The Lens Formula
Light rays passing through a convex lens converge at a point behind the lens, which is considered the positive direction in a coordinate system placed at the optical center (O). For a concave lens, light rays appear to diverge from a virtual focus located on the same side as the object, placing it in the negative direction.
Convex lens focal length is always positive.
Concave lens focal length is always negative.
The optical center of the lens acts as the origin (0,0) of the Cartesian coordinate system.
Sign conventions provide a systematic way to solve lens problems without confusion.
Designing spectacles for vision correction (e.g., Myopia uses concave lenses).
Calculating image position in microscopes and telescopes.
| Feature | Convex Lens | Concave Lens |
|---|---|---|
Focal Length (f) | Positive (+) | Negative (-) |
A real image formed by a lens is inverted and has a negative image height.
Option C is 'positive; negative', which correctly matches Convex; Concave respectively.
C is correct тАФ According to sign conventions, the focal length of a convex lens is positive and that of a concave lens is negative.
Remember that 'Convex' starts with C but behaves 'Positive', whereas 'Concave' is 'Negative'. This applies to both mirrors and lenses.
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