An object is placed 10m from a pinhole camera of length 25cm. Calculate the linear magnification.

1. Analyze the question

We are given:

• Object distance ($u$) = 10 m
• Image distance/Camera length ($v$) = 25 cm
• We need to find the linear magnification ($m$).

2. Explain the concept

In a pinhole camera, the magnification ($m$) is defined as the ratio of the image height to the object height, which is also equivalent to the ratio of the image distance ($v$) to the object distance ($u$).

The formula is:

Important Note: Before calculating, you must ensure that both distances are in the same unit. We will convert the object distance from meters (m) to centimeters (cm).

3. Show the solution

Step 1: Convert units

• $u = 10 \text{ m} = 10 \times 100 \text{ cm} = 1000 \text{ cm}$
• $v = 25 \text{ cm}$

Step 2: Apply the formula

Step 3: Simplify the fraction

Step 4: Express in standard form To convert $0.025$ to standard form: Move the decimal point 2 places to the right to get 2.5. Since we moved it 2 places to the right, we multiply by $10^{-2}$.

4. Identify the answer

Comparing our result to the given options: A. $2.5 \times 10^2$ B. $2.5 \times 10^{-2}$ C. $2.5 \times 10^{-1}$ D. $2.5 \times 10^1$

The correct option is B.

5. Tip

Always check your units first! A very common mistake in JAMB Physics is forgetting to convert meters to centimeters or vice versa. If you had divided 25 by 10, you would have gotten 2.5, which would lead you to choose the wrong option. Always ensure your $u$ and $v$ are in the same units before dividing.