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 $3.5mm$ . What is the estimate on the thickness of hair?

A) $0.035mm$

B) $0.007mm$

C) $3.5mm$

D) None of the Above

Answer 1

Start by describing a microscope and the magnification it produces. Then move on to describe the relation between width of actual hair, observed width and the magnification of a microscope. Use this concept to reach the solution.

Complete Step By Step Answer:

A microscope is an optical instrument, specifically designed to view objects that are too small to be seen by the naked eye. A microscope magnifies an object and to achieve this microscopes use a combination of lenses (convex or concave) to form a highly enlarged image.

A point to note in the given problem is that the students made $20$ observations and calculated the average observed width of the hair. This is a good example of how to make a scientific observation. We have to take multiple observations and then calculate an average.

Let the original width of hair be $W$.

In this problem, it is given that the microscope has a magnification$(M)$ power of $100$ and the observed width of hair is $3.5mm$.

We know that, Width of magnified hair $= W \times M$

$\Rightarrow 3.5 = W \times 100$

$\Rightarrow W = \dfrac{{3.5}}{{100}}$

$\Rightarrow W = 0.035mm$

Hence, option (A) is the correct choice.

Note: We have multiple types of microscopes, most common are the light microscope and electron microscope. As the name suggests light microscope uses light to form the image and electron microscope uses a beam of light. The light microscope has a general magnification of 40x-100x and an electron microscope can achieve a magnification of up to 10,000,000x.