Question

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 ?

Answer 1

Given:

Magnification of microscope, M = 100
Average width of hair seen in the microscope = 3.5 mm
Number of observations = 20 (used to improve reliability)

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Step 1: Use definition of magnification

Magnification is given by:

M = (Image size) / (Actual size)

So, actual thickness of hair:

Thickness = (Image width) / M

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Step 2: Calculate thickness of the hair

Thickness = 3.5 mm / 100

Thickness = 0.035 mm

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Step 3: Express in standard units

0.035 mm = 3.5 × 10⁻² mm

= 3.5 × 10⁻⁵ m

= 35 μm

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Final Answer:

The estimated thickness of the human hair is
0.035 mm ≈ 3.5 × 10⁻⁵ m (35 μm)