An object at 25cm from the eye sustend an angle 10at the eye. When observed it through a simplemicroscope at normal adjustment, the angle that the image substend at the eye becomes 110. Thefocal length of the lens.
Question
An object at 25cm from the eye sustend an angle 10at the eye. When observed it through a simplemicroscope at normal adjustment, the angle that the image substend at the eye becomes 110. Thefocal length of the lens.
Solution
The magnifying power of a simple microscope at normal adjustment is given by the formula:
1 + (D/f)
where D is the near point (usually taken as 25 cm for a normal eye) and f is the focal length of the lens.
The magnifying power can also be defined as the ratio of the angle subtended by the image to the angle subtended by the object at the eye. In this case, it is given as 110/10 = 11.
So, we can set up the equation:
11 = 1 + (25/f)
Solving for f gives:
f = 25/(11 - 1) = 25/10 = 2.5 cm
So, the focal length of the lens is 2.5 cm.
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