An object placed in front of a lens, forms a virtual image whose magnifications is 0.5. The focal length of the lens is 30cm. Calculate the object distance.(with sign)
Question
An object placed in front of a lens, forms a virtual image whose magnifications is 0.5. The focal length of the lens is 30cm. Calculate the object distance.(with sign)
Solution
To solve this problem, we can use the lens formula and the magnification formula.
The lens formula is 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance.
The magnification formula is m = -v/u, where m is the magnification, v is the image distance, and u is the object distance.
Given that the magnification m is 0.5 and the focal length f is 30 cm, we can substitute these values into the magnification formula to find the image distance v.
0.5 = -v/u
Solving for v gives v = -0.5u.
We can then substitute this value for v into the lens formula:
1/30 = 1/(-0.5u) - 1/u
Solving this equation for u gives u = -60 cm.
The negative sign indicates that the object is on the same side of the lens as the light source, which is consistent with the formation of a virtual image. Therefore, the object distance is -60 cm.
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