A simple microscope has a magnifying power of 3.0 .when the image is formed at the near point (25cm) of a normal eye . A-what is its focal length ? B-what will be its magnifying power if the image is formed at infinity

To tackle this question, we need to break it down into two parts: first, we'll find the focal length of the simple microscope, and then we'll determine its magnifying power when the image is formed at infinity. Let's dive into the details!

Finding the Focal Length

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

• M = D / f

Here, D is the near point distance (which is typically 25 cm for a normal eye), and f is the focal length of the lens. Given that the magnifying power (M) is 3.0, we can rearrange the formula to solve for the focal length:

• f = D / M

Substituting the known values:

• f = 25 cm / 3.0
• f = 8.33 cm

Thus, the focal length of the simple microscope is approximately 8.33 cm.

Calculating Magnifying Power at Infinity

Next, let's find the magnifying power when the image is formed at infinity. The formula for magnifying power in this case is slightly different:

• M = 1 + (D / f)

Using the focal length we just calculated (8.33 cm), we can substitute it into the formula:

• M = 1 + (25 cm / 8.33 cm)

Now, let's do the math:

• M = 1 + 3.0
• M = 4.0

Therefore, the magnifying power of the microscope when the image is formed at infinity is 4.0.

Summary of Findings

In summary, we found that:

• The focal length of the simple microscope is approximately 8.33 cm.
• The magnifying power when the image is formed at infinity is 4.0.

This understanding of magnifying power and focal length is crucial in optics, especially when dealing with lenses and microscopes. If you have any further questions or need clarification on any of these concepts, feel free to ask!