A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of hair?

To find the actual thickness (or width) of the human hair, we need to understand the relationship between the actual size of an object, its observed size under a microscope, and the magnification of the microscope.

The formula relating these quantities is given by:
$\text{Magnification}=\frac{\text{Observed size (Apparent width)}}{\text{Actual size (Real width)}}$
From this relationship, we can express the actual thickness of the hair as:
$\text{Actual size}=\frac{\text{Observed size (Apparent width)}}{\text{Magnification}}$

We are given the following values:
• Magnification of the microscope = 100
• Average observed width of the hair in the field of view = 3.5 mm

Substituting these values into our formula:
$\text{Estimate of the thickness of hair}=\frac{3.5\text{mm}}{100}$
$=0.035\text{mm}$

Therefore, the estimated thickness of the human hair is 0.035mm.