Problem 60 - Master Resource Book in JEE Main Physics

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 \(3.5 \mathrm{~mm}\). The thickness of hair isfNCERT] (a) \(0.035 \mathrm{~mm}\) (b) \(0.04 \mathrm{~mm}\) (c) \(0.35 \mathrm{~mm}\) (d) \(0.40 \mathrm{~mm}\)

Step-by-Step Solution

Answer

The thickness of the hair is 0.035 mm, option (a).

Step 1: Understanding the Problem

The student measures the width of a hair using a microscope with a magnification factor of 100. The average width observed under the microscope is 3.5 mm. The task is to find out the actual thickness of the hair.

Step 2: Calculating the Actual Thickness

Since the microscope magnifies the view by 100 times, the observed measurement needs to be divided by the magnification factor to find the real thickness. Thus, the actual thickness of the hair is calculated by dividing 3.5 mm by the magnification factor of 100.

Step 3: Performing the Division

Compute the actual thickness of the hair using the formula: Actual thickness = Observed thickness / Magnification. Therefore, Actual thickness = \( \frac{3.5 \, \text{mm}}{100} \).

Step 4: Simplifying the Expression

Calculate \( \frac{3.5}{100} \). Divide 3.5 by 100 to obtain 0.035 mm.

Step 5: Identifying the Correct Option

Compare the calculated thickness, 0.035 mm, with the options provided: (a) 0.035 mm, (b) 0.04 mm, (c) 0.35 mm, (d) 0.40 mm. The correct choice is option (a) 0.035 mm.

Key Concepts

Microscope Magnification

When you first hear about microscopes, they sound a bit like magic. But they're just super useful tools in science that help us see the tiny things we can't see with our eyes alone. Imagine if you had to draw your favorite cartoon character, but as tiny as an ant. Hard, right? Microscopes make this easy by magnifying, or blowing up, those tiny things so much that we can see them clearly. When we say a microscope has a magnification of 100, it means the object you are looking at appears 100 times bigger than its real size.
In the exercise, our student used a microscope with a 100 magnification factor to see the hair much larger than its actual size. Understanding this magnification factor helps in calculating the real size of the small object being observed, like the thickness of the hair in our activity.

Physics Problem Solving

Solving physics problems is like being a detective, searching for clues and piecing together the puzzle. We start by understanding the given data and what is being asked. In this exercise, we know the observed width of hair and we need to find its actual thickness. We use the methodical approach to break down the problem into small steps.

• Step 1: Gather all known information, like the magnification factor and the measured width.
• Step 2: Apply relevant physics principles or formulas, such as using magnification to relate observed and actual sizes.

By using such structured approaches in physics, we arrive at logical and correct solutions, making sure that every theory fits within its context to guide us to the right answer.

Division as Mathematical Operation

Division in math might sound simple, but it plays a key role in many scientific calculations. It's like sharing equally among a group. When you divide one number by another, you are essentially figuring out how many times one number can be "spread" over or fit into another.
In the context of our exercise, we took the observed measurement, which was 3.5 mm, and used division to factor out the magnification effect. Hence, we divided 3.5 mm by the magnification factor, 100, to find out how thick the hair actually was. This division operation helped us calculate the actual thickness of the hair to be 0.035 mm, meaning it is quite thin and almost thread-like.

Observation in Scientific Experiment

Observations made during scientific experiments are like clues in a mystery novel. They're bits of information we gather to understand what's really going on. In the exercise, the student made observations using a microscope, noting that under magnification, the hair appeared to be 3.5 mm wide. This kind of observation forms the base of any experiment, and caring for accuracy ensures reliable results.
Making observations requires attention to detail and careful noting down of what one sees. From this, scientists can deduce facts about the physical world around them. In this way, observations made during experiments help conclude the facts, supporting the process of gathering data and verifying hypotheses in scientific study.