Question

The sun is 150,000,000 km from earth; its diameter is 1,400,000 km. A student uses a 4.6-cm-diameter lens with f = 10 cm to cast an image of the sun on a piece of paper. What is the diameter of the image on the paper?

Answer 1

The diameter of the image of the sun on the paper is approximately 1.65 x 10^(-12) cm.

Step-by-step explanation:

To find the diameter of the image of the sun on the paper, we can use the concept of similar triangles. The ratio of the diameter of the image to the diameter of the lens is equal to the ratio of the distance of the image to the lens to the distance of the sun from the lens. Let's calculate:

Step 1: Calculate the ratio of the distances:

Distance of image to lens: 10 cm - 4.6 cm = 5.4 cm

Distance of sun from lens: 150,000,000 km

Ratio of distances: 5.4 cm / 150,000,000 km = 5.4 cm / 1,500,000,000,000 cm = 1 / 278,000,000,000

Step 2: Calculate the diameter of the image:

Diameter of lens: 4.6 cm

Diameter of image: x

Ratio of diameters: x / 4.6 cm = 1 / 278,000,000,000

Solving for x: x = 4.6 cm / 278,000,000,000 = 1.65 x 10^(-12) cm

Therefore, the diameter of the image of the sun on the paper is approximately 1.65 x 10^(-12) cm.