A magnifying glass of focal length 10 cm is used to read letters of thickness 0.5 mm held 8 cm away from the lens. Calculate the image size. How big will the letters appear? Can you read the letters if held 5 cm away from the lens? If yes, of what size would the letters appear? If no, why not?
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Given that, f = +10 cm, u = -8 cm,
From thin lens formula,
\(\frac{1}{f}=\frac{1}{\text{v}}-\frac{1}{u}\)
∴ \(\frac{1}{10}=\frac{1}{\text{v}}-\frac{1}{-8}\)
∴ v = 40 cm
Magnification of a lens is,
m = \(\frac{v}{u}=\frac{Object\,size\,h-i}{Object\,size\,h-0}\)
∴ \(\frac{40}{8}=\frac{h_1}{0.5}\)
∴ h1 = 2.5 cm
This implies the height of the image is 5 times that of the object.
Magnifying power,
M = \(\frac{D}{u}=\frac{25}{8}\) = 3.125
∴ Image will appear to be 3.125 times bigger,
i.e., 3.125 × 0.5 = 1.5625 cm
For u = -5 cm, v will be -10 cm
For an average human being to see clearly,
the image must be at or beyond 25 cm. Thus it will not possible to read the letters if held 5 cm away from the lens.