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Class 11 NCERT PHYSICS • Chapter 1: Units and Measurement • Question 7

NCERT Solutions

|Class 11 NCERT PHYSICS›Units and Measurement›Question 7

CHAPTER 01

Units and Measurement

17 Questions

QUESTION 7

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?

SOLUTION

We need to determine the actual thickness of a hair by dividing its magnified average width by the microscope magnification.

Concept: Linear magnification

The linear magnification ( $M$ ) of a microscope is defined as the ratio of the apparent (observed) size of the object to its actual physical size.

M = \frac{\text{Observed width}}{\text{Actual thickness}}

Given:

Magnification ( $M$ ) = $100$
Average observed width ( $w_{\text{obs}}$ ) = $3.5\,\text{mm}$
Number of observations ( $n$ ) = $20$ (used to determine the average width)

Solving:

To find the actual thickness ( $t$ ), we rearrange the magnification formula:

t = \frac{w_{\text{obs}}}{M}

Substitute the known values into the equation:

\begin{aligned} t &= \frac{3.5\,\text{mm}}{100} \\ &= 0.035\,\text{mm} \end{aligned}

Answer

0.035\,\text{mm}