By what factor will the size of an object placed 10cm from a convex lens be increased if the image is seen on a screen placed 25cm from the lens?
Form the lens formula = \(\frac{1}{\text{U}}\) + \(\frac{1}{\text{V}}\) = \(\frac{1}{\text{f}}\)
=> \(\frac{1}{10} + \frac{1}{25}\) = \(\frac{1}{\text{f}}\)
∴ \(\frac{(5 + 2)}{50}\) = \(\frac{1}{\text{f}}\)
∴ f = \(\frac{50}{7}\)cm
Since the image is observed on a screen, it is a real image. Thus magnification
M =\(\frac{\text{f}}{U - f}\)
= \(\frac{\frac{50}{7}}{10 - \frac{50}{7}}\)
∴ M = \(\frac{\frac{50}{7}}{\frac{20}{7}}\)
= \(\frac{50}{7}\) x \(\frac{7}{20}\) = 2.5
Or
m = \(\frac{\text{v}}{\text{u}}\)
= \(\frac{25}{10}\) = 2.5
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