A lens of focal length 1500 mm is used to project an image of the Sun onto a screen. If the Sun subtends an angle of 0.50° in the sky, what is the diameter of the image on the screen?
A) 60 mm
B) 30 mm
C) 26 mm
D) 6.5 mm
E) 13 mm

Question

Quizplus · Accepted Answer

The diameter of the image can be calculated using the formula for linear size in a projection, $d = f \times \tan(\theta)$, where $d$ is the diameter of the image, $f$ is the focal length of the lens, and $\theta$ is the angle subtended by the object (in radians). First, convert the angle from degrees to radians: $0.50° = 0.50 \times \frac{\pi}{180} = \frac{\pi}{360}$ radians. Then, calculate the diameter: $d = 1500 \times \tan\left(\frac{\pi}{360}\right) \approx 13$ mm.

A Lens of Focal Length 1500 Mm Is Used to Project