Question

In a cinema, a picture 2.5 cm wide on the film is projected to an image 3.0 m wide on a screen that is 18 m away. The focal length of the lens is about:

• A. 7.5 cm
• B. 10 cm
• C. 12.5 cm
• D. 15 cm

Hint:

The magnification formula helps to relate the size of the image and object to the focal length and distances in lens systems.

Answer 1

The Correct Option is D

The magnification \( M \) is given by: \[ M = \frac{\text{Image Height}}{\text{Object Height}} = \frac{\text{Image Distance}}{\text{Object Distance}} \] From the problem, we know that: \[ M = \frac{3.0 \, \text{m}}{2.5 \, \text{cm}} = 120 \] Using the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where \( f \) is the focal length, \( v \) is the image distance, and \( u \) is the object distance. Since \( M = \frac{v}{u} \), we can solve for \( v \) and substitute into the lens equation to find the focal length.
After solving, we find \( f \approx 15 \, \text{cm} \).
Thus, the correct answer is (d).