a person uses +1.5d glasses to have normal vision from 25cm onwards .he uses a +20D lens as simple microscope to see an object. what is the maximum magnifying power if he uses the microscope without glasses?

To determine the maximum magnifying power of a +20D lens when used as a simple microscope without glasses, we need to understand a few key concepts related to optics, particularly the relationship between the focal length of the lens and the magnification it provides.

Understanding Lens Power and Focal Length

The power of a lens (measured in diopters, D) is related to its focal length (f) in meters by the formula:

Power (D) = 1 / Focal Length (m)

For a +20D lens, we can calculate the focal length:

• Focal Length (f) = 1 / Power = 1 / 20 = 0.05 meters or 5 cm

Calculating Magnifying Power

The magnifying power (M) of a simple microscope can be calculated using the formula:

M = (D + 1) / D

Where D is the distance of the near point of distinct vision from the lens. For a person with normal vision, this distance is typically taken as 25 cm (or 0.25 m). However, since the person in question uses +1.5D glasses to see clearly at 25 cm, we need to adjust our calculations accordingly.

Adjusting for the Near Point

When using the microscope without glasses, the effective near point for this individual is still 25 cm. However, since they are using a +20D lens, we can directly calculate the magnifying power based on the focal length we found earlier.

Using the formula for magnifying power:

• Near point (D) = 25 cm = 0.25 m
• Focal length (f) = 5 cm = 0.05 m

Now, substituting these values into the magnifying power formula:

M = (D / f) = (0.25 m / 0.05 m) = 5

Final Thoughts on Magnification

Thus, the maximum magnifying power of the +20D lens when used as a simple microscope without glasses is 5 times. This means that the object viewed through the microscope will appear five times larger than it does to the naked eye at the near point of distinct vision.

In summary, understanding the relationship between lens power, focal length, and magnifying power allows us to calculate how effectively a lens can magnify an object. In this case, the +20D lens provides a significant magnification, enhancing the viewer's ability to see fine details clearly.