If the focal length of a camera is 20cm, the distance from the film at which the lens must be set to produce a sharp image of 100cm away is

Analysis

To solve this problem, we need to apply the Lens Formula, which relates the focal length ($f$), the object distance ($u$), and the image distance ($v$). In a camera, the "film" acts as the screen where the image is formed.

Concept

The lens formula is given by:

Where:

• $f$ = focal length of the lens
• $u$ = distance of the object from the lens
• $v$ = distance of the image (the film) from the lens

Step-by-Step Solution

1. Identify the given values: • Focal length ($f$) = $20\text{ cm}$ • Object distance ($u$) = $100\text{ cm}$ • Image distance ($v$) = ?

2. Rearrange the formula to solve for $v$: $$\frac{1}{v} = \frac{1}{f} - \frac{1}{u}$$

3. Substitute the values into the equation: $$\frac{1}{v} = \frac{1}{20} - \frac{1}{100}$$

4. Find a common denominator (which is 100): $$\frac{1}{v} = \frac{5}{100} - \frac{1}{100}$$ $$\frac{1}{v} = \frac{4}{100}$$

5. Solve for $v$: $$\frac{1}{v} = \frac{1}{25}$$ $$v = 25\text{ cm}$$

The lens must be set at a distance of $25\text{ cm}$ from the film to produce a sharp image.

Conclusion

Comparing our result to the options provided, the correct choice is C.

Exam Tip

When dealing with lens and mirror problems, always remember the sign convention:

• Real images (like those formed on a camera film) have a positive image distance ($v$).
• Virtual images have a negative image distance ($v$).
• If you ever get a negative result for $v$ in a calculation where you expected a real image, double-check your arithmetic!