A simple magnifier is made using a single convex lens by placing the object closer than the focal point. To maximise the magnification the object is placed so the image is formed at the near point. By convention this is taken to be 0.25 m from the lens.For a lens with focal length f = 0.08 m, calculate the magnification produced. (You will first need to calculate the object distance, o, required to produce a virtual image at the near point i= -0.25 m.)Express answer to two decimal places.
Question
A simple magnifier is made using a single convex lens by placing the object closer than the focal point. To maximise the magnification the object is placed so the image is formed at the near point. By convention this is taken to be 0.25 m from the lens.For a lens with focal length f = 0.08 m, calculate the magnification produced. (You will first need to calculate the object distance, o, required to produce a virtual image at the near point i= -0.25 m.)Express answer to two decimal places.
Solution
To solve this problem, we first need to use the lens formula, which is 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance.
Given that f = 0.08 m and v = -0.25 m (the negative sign indicates that the image is virtual and on the same side as the object), we can substitute these values into the lens formula to find u:
1/0.08 = 1/-0.25 - 1/u
Solving for 1/u gives us:
1/u = 1/0.08 + 1/0.25
Calculating the above expression gives us approximately 1/u = 16.25.
Therefore, u = 1/16.25 ≈ -0.06 m (the negative sign indicates that the object is on the same side as the light source).
Next, we calculate the magnification, which is given by the formula m = -v/u.
Substituting v = -0.25 m and u = -0.06 m into the formula gives us:
m = -(-0.25)/-0.06 ≈ 4.17
Therefore, the magnification produced by the simple magnifier is approximately 4.17 (to two decimal places).
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