A simple microscope is a combination of two lenses in contact. Their powers are + 20 D and − 4 D . The distance of distinct vision is 25 cm . When seen through the microscope, the size of the image of

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A simple microscope is a combination of two lenses in contact. Their powers are + 20 D and − 4 D . The distance of distinct vision is 25 cm . When seen through the microscope, the size of the image of an object 3 mm high is

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The equivalent power of the lens combination is given by the sum of their individual powers:

$P = P_{1} + P_{2} = + 20 D - 4 D = + 16 D$

The focal length of the combination is:

$f = \frac{1}{P} = \frac{1}{16} m = \frac{100}{16} cm = 6.25 cm$

For a simple microscope, when the image is formed at the least distance of distinct vision ( $D = 25 cm$ ), the linear magnification $m$ is given by:

$m = 1 + \frac{D}{f}$

Substituting the values:

$m = 1 + \frac{25}{6.25} = 1 + 4 = 5$

The size of the image $h_{i}$ is the magnification times the size of the object $h_{o}$ :

$h_{i} = m \times h_{o} = 5 \times 3 mm = 15 mm$

Converting to centimeters:

$h_{i} = 1.5 cm$

Answer: $1.5 cm$

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