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An object 3 cm high is placed at a distance of 30 cm from a convex lens of focal length 20 cm. What is the magnification produced?
1
2
2
0.5
2
The magnification (m) for a lens is given by the ratio of image distance (v) to object distance (u). Using the lens formula, we find the image distance, and subsequently calculate the magnification ratio.
The magnification (m) for a lens is given by the ratio of image distance (v) to object distance (u). Using the lens formula, we find the image distance, and subsequently calculate the magnification ratio.
A convex lens acts like a magnifying glass; when you move an object close to the focal point, the image flips and enlarges, just like how a camera lens focuses light onto a sensor.
f1тАЛ=v1тАЛтИТu1тАЛ тАФ Lens Formula
m=uvтАЛ=hoтАЛhiтАЛтАЛ тАФ Magnification Formula
The lens formula is f1тАЛ=v1тАЛтИТu1тАЛ. With f=+20┬аcm and u=тИТ30┬аcm (sign convention), we get v1тАЛ=201тАЛ+тИТ301тАЛ=603тИТ2тАЛ=601тАЛ. Thus, v=60┬аcm. Magnification m=uvтАЛ=тИТ3060тАЛ=тИТ2. Note: The question implies magnitude or uses specific conventions; however, purely calculation-wise, m=тИТ2. Given the options, there is an error in the provided answer key as the correct value is тИТ2.
For a convex lens, if f<u<2f, the image formed is real, inverted, and magnified.
Sign convention: u is negative, f is positive for convex lenses.
A magnification of тИТ2 indicates the image is inverted and twice the size of the object.
Provides clear magnification ratios for optical design.
Standard lens formula assumes thin lens approximation.
Camera lenses
Microscopes
The provided answer '1' is mathematically incorrect based on the given parameters u=30 and f=20.
At u=2f (i.e., 40┬аcm), the magnification would be тИТ1, leading to a magnitude of 1.
B is correct тАФ Using the lens formula, the magnification is calculated to be -2, implying the magnitude is 2.
Always verify the sign of u as negative in lens problems; ignoring this is the most common cause of calculation errors in competitive exams.